Phase-modulating apparatus

ABSTRACT

A phase-modulating apparatus includes a spatial light modulator, an input value setting unit, a plurality of sets of reference data, a converting unit, and a driving unit. The input value setting unit sets an input value for each pixel. Each set of reference data corresponds to at least one pixel. The converting unit converts an input value inputted for each pixel to a control value by referencing the corresponding set of reference data. The driving unit converts the control value to a voltage value. The driving unit drives each pixel with a drive voltage corresponding to the voltage value. Each set of reference data correlates a plurality of first values from which input values are taken, and a plurality of second values from which control values are taken to ensure that the relationship between the plurality of first values and phase modulation amounts attained by the corresponding at least one pixel is a prescribed linear relationship.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a phase-modulating apparatus and amethod for setting the phase-modulating apparatus.

2. Description of the Related Art

A spatial light modulator (SLM) using liquid crystal on silicon (LCoS)is well known in the art. When a voltage is applied to a pixelelectrode, liquid crystal molecules in the LCoS rotate within a verticalplane of the substrate, modifying the phase modulation amount ofincident light. However, since the phase modulation amount changesnonlinearly relative to voltage applied to the pixel electrode, it hasnot been possible to obtain a desired phase modulation amount.

SUMMARY OF THE INVENTION

FIG. 1 shows a conceivable LCoS spatial light modulator. Since LCoSsilicon substrate 21 is formed in semiconductor processes, the siliconsubstrate 21 cannot be made thick and therefore have a low mechanicalstrength. Hence, as shown in FIG. 1, stress generated during processesfor manufacturing LCoS elements can distort a silicon substrate 21reducing the flatness of the LCoS mirror surface. Further, the thicknessof a liquid crystal layer 27 is not uniform in the LCoS, and the phasemodulation amount for each pixel differs according to the thickness ofthe liquid crystal layer 27. Hence, the wavefront of light reflected offthe LCoS SLM is greatly distorted due to irregularities in the thicknessof the liquid crystal layer 27 and distortion in the reflecting surface,resulting in different phase modulation amounts for each pixel. Morespecifically, the phase modulation amount Φ(V, x, y) is represented bythe following equation, where a pixel position in the x and y directionis given by (x, y) and V is voltage.

Φ(V,x,y)=φ(V,x,y)+Φ_(o)(x,y)  (1)

Based on this equation, the phase modulation amount Φ(V, x, y) isobtained by adding φ(V, x, y) that depends on voltage to an amount Φ₀(x,y) that is independent on voltage. Here, φ(v, x, y) is expressed by thefollowing equation.

φ(V,x,y)=2Δn(V)d(x,y)  (2)

In the above equation, Δn(V) is the birefringence index for thepolarization component whose electric field that oscillates in adirection parallel to the liquid crystal orientation; and d(x, y) is thethickness of the liquid crystal layer 27 at position (x, y). Hence, φ(V,x, y) is dependent on the thickness d(x, y) of the liquid crystal layer,and differs according to pixel. Further, the relationship betweenvoltage V and φ(V, x, y) is nonlinear for each pixel. On the other hand,Φ₀(x, y) is primarily attributed to distortion in the LCoS reflectingsurface (silicon substrate 21). Hereafter, the nonlinearity of the phasemodulation amount in relation to the voltage and irregularities in phasemodulation amount for each pixel caused by irregularities in d(x, y)will be collectively referred to as the voltage-dependent phasemodulation characteristics. In other words, the voltage-dependent phasemodulation characteristics indicate the property of φ(V, x, y) in thephase modulation amount Φ(V, x, y). Further, irregularities in phasemodulation amount for each position (x, y) caused by distortion in theLCoS reflecting surface, which is indicated by Φ₀(x, y), will bereferred to as voltage-independent distortion.

Various methods have been proposed for correcting phase modulationcharacteristics, such as “Phase Calibration of Spatially NonuniformSpatial Light Modulator [Applied Opt., vol. 43, No. 35, December 2004](hereinafter referred to as reference 1) or “Improving Spatial LightModulator Performance through Phase Compensation” [Proc. SPIE, vol.5553, October 2004] (hereinafter referred to as reference 2).

Further, in a method disclosed in International publicationWO2003/036368, the voltage independent-distortion is calibrated by usinga pattern for canceling distortion. The pattern is obtained by measuringwavefront distortion in a two-beam interferometer using the phasemodulating SLM.

In the LCoS SLM of references 1 and 2, calibration is performed aftermeasuring wavefront distortion using a two-beam interferometer. However,measurements taken with the two-beam interferometer combinevoltage-dependent phase modulation characteristics withvoltage-independent distortion. Further, the method in reference 1 doesnot perform correct calibration of nonlinearity, merely extractingregions from nonlinear characteristics that approach relative linearity.

Reference 2 uses a single look-up table to calibrate nonlinearity forall pixels. Hence, this method cannot correct irregularities in phasemodulation amount among each pixel caused by voltage-dependent phasemodulation characteristics. As a result, this method is less accuratewhen calibrating an LCoS SLM having severe distortion.

It is an object of the present invention to provide a phase-modulatingapparatus capable of accurately calibrating voltage-dependent phasemodulation characteristics and voltage-independent distortion and amethod for setting the phase modulation apparatus.

In order to attain the above and other objects, the invention provides aphase-modulating apparatus. The phase-modulating apparatus includes aspatial light modulator, an input value setting unit, a plurality ofsets of reference data, a converting unit, and a driving unit. Thespatial light modulator includes a plurality of pixels arranged adjacentto one another two-dimensionally. Each pixel is capable ofphase-modulating input light in response to application of a drivevoltage. The input value setting unit sets an input value for eachpixel. Each set of reference data corresponds to at least one pixel. Theconverting unit converts an input value inputted for each pixel to acontrol value by referencing the corresponding set of reference data.The driving unit converts the control value to a voltage value. Thedriving unit drives each pixel with a drive voltage corresponding to thevoltage value. Each set of reference data correlates a plurality offirst values from which input values are taken, and a plurality ofsecond values from which control values are taken to ensure that therelationship between the plurality of first values and phase modulationamounts attained by the corresponding at least one pixel is a prescribedlinear relationship.

According to another aspects, the invention provides a method forsetting a phase-modulating apparatus. The phase-modulation apparatusincludes, a spatial light modulator including a plurality of pixelsarranged adjacent to one another two-dimensionally, each pixel beingcapable of phase-modulating input light in response to application of adrive voltage, an input value setting unit setting an input value foreach pixel, and a driving unit converting the control value to a voltagevalue, the driving unit driving each pixel with a drive voltagecorresponding to the voltage value. The method includes creating aplurality of sets of reference data, the creating step includes,measuring phase modulation amounts, for at least one pixel, denoting thevoltage-dependent phase modulation characteristics, generating aplurality of sets of reference data, based on the voltage-dependentphase modulation characteristics, such that each set of reference datacorresponds to at least one pixel and that each set of reference datacorrelates a plurality of first values from which input values aretaken, and a plurality of second values from which control values aretaken to ensure that the relationship between the plurality of firstvalues and phase modulation amounts attained by the corresponding atleast one pixel is a prescribed linear relationship, and setting theconvert unit to convert, for each pixel, the control value to thevoltage value by referencing the corresponding set of reference data.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 is an explanatory diagram illustrating distortion in the LCoSreflecting surface of a conceivable phase-modulating apparatus;

FIG. 2 is a block diagram showing the structure of an LCoS phasemodulator according to a first embodiment of the present invention;

FIG. 3 is an explanatory diagram showing the structure of a LCoS spatiallight modulator;

FIG. 4(A) is an explanatory diagram showing the state of liquid crystalmolecules in the LCoS spatial light modulator when there's no potentialdifference between pixel electrodes and an opposing electrode;

FIG. 4(B) is an explanatory diagram showing the state of liquid crystalmolecules in the LCoS spatial light modulator when there's a relativelysmall potential difference between pixel electrodes and the opposingelectrode;

FIG. 4(C) is an explanatory diagram showing the state of liquid crystalmolecules in the LCoS spatial light modulator when there's a relativelylarge potential difference between pixel electrodes and the opposingelectrode;

FIG. 5 is an explanatory diagram showing a look-up table (LUT) accordingto the first embodiment;

FIG. 6 is an explanatory diagram illustrating conversion with a D/Acircuit;

FIG. 7 is a flowchart illustrating steps in a method of phase modulationusing the LCoS phase modulator according to the first embodiment;

FIG. 8 is a flowchart illustrating steps in a method of setting minimumand maximum values of voltage for driving the LCoS spatial lightmodulator;

FIG. 9 is an explanatory diagram showing the structure of a polarizationinterferometer;

FIG. 10 is a graph showing the relationship of DA input values and thephase modulation amount;

FIG. 11 is a graph showing the relationship between the DA input valuesand the phase modulation amount after setting minimum and maximum valuesfor the voltage;

FIG. 12 is a flowchart illustrating steps in a method of creating theLUT;

FIG. 13 is a graph showing the relationship between control input valuesobtained by calibrating the voltage-dependent phase modulationcharacteristics using the LUT, and the phase modulation amount;

FIG. 14 is an explanatory diagram showing the structure of a Michelsoninterferometer;

FIG. 15 is a flowchart illustrating steps in a method of forming acalibration pattern;

FIG. 16 is an explanatory diagram showing a calibration pattern createdaccording to the method in FIG. 15;

FIG. 17(A) is an explanatory diagram showing the results of performingphase modulation by applying the LUT and the calibration pattern;

FIG. 17(B) is an explanatory diagram showing the results of performingphase modulation without using the LUT and the calibration pattern;

FIG. 18 is an explanatory diagram showing the structure of an LCoSspatial light modulator according to a first variation of the firstembodiment;

FIG. 19 is a block diagram showing the structure of an LCoS phasemodulator according to a second variation of the first embodiment;

FIG. 20 is a block diagram showing the structure of an LCoS phasemodulator according to a third variation of the first embodiment;

FIG. 21 is an explanatory diagram of an LUT including calibrationpattern data according to a seventh variation of the first embodiment;

FIG. 22 is a block diagram showing the structure of an LCoS spatialphase modulator according to a second embodiment of the presentinvention;

FIG. 23 is an explanatory diagram showing one example of an LUT map;

FIG. 24 is an explanatory diagram showing another example of the LUTmap;

FIG. 25 is an explanatory diagram showing another example of the LUTmap;

FIG. 26 is an explanatory diagram of an LUT according to the secondembodiment;

FIG. 27 is a flowchart illustrating steps in a method of phasemodulation according to the LCoS phase modulator according to the secondembodiment;

FIG. 28 is a flowchart illustrating steps in a method of creating an LUTmap;

FIG. 29 is a flowchart illustrating steps in a method of creating an LUTaccording to the second embodiment;

FIG. 30 is a block diagram showing the structure of an LCoS phasemodulator according to a third variation of the second embodiment;

FIG. 31 is a block diagram showing the structure of an LCoS phasemodulator according to a fourth variation of the second embodiment;

FIG. 32 is an explanatory diagram of an LUT including calibrationpattern data according to a eleventh variation of the second embodiment;

FIG. 33(A) is an explanatory diagram illustrating the thickness of aliquid crystal layer in the LCoS spatial light modulator;

FIG. 33(B) is an explanatory diagram illustrating the thickness of theliquid crystal layer and tilt in the glass substrate of the LCoS spatiallight modulator; and

FIG. 34 is a flowchart illustrating steps in a method of creating an LUTmap according to a variation of a twelfth variation of the secondembodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Next, preferred embodiments of the present invention will be describedwhile referring to the accompanying drawings.

First Embodiment

First, a first embodiment of the present invention will be describedwith reference to FIGS. 2 through 17(B). As shown in FIG. 2, an LCoSphase modulator 1 according to the first embodiment includes an LCoSspatial light modulator 2, a drive unit 3 for applying voltages to theLCoS spatial light modulator 2, and a control unit 4 for transmittingdata, such as a control input value as described later, to the driveunit 3.

As shown in FIG. 3, the LCoS spatial light modulator 2 includes asilicon substrate 21, a spacer 26, and a glass substrate 25 bonded tothe silicon substrate 21 via the spacer 26. The space formed between thesilicon substrate 21 and glass substrate 25 is filled with a liquidcrystal layer 27 having liquid crystal molecules 28. A plurality ofpixel electrodes 22, and a circuit (not shown) for controlling thevoltage applied to the pixel electrodes 22 are formed on the siliconsubstrate 21. An orientation layer 23 is formed over the pixelelectrodes 22. The glass substrate 25 includes an opposing electrode 24and another orientation layer 23. The electrode 24 opposes the pixelelectrodes 22 through the liquid crystal layer 27. The liquid crystalmolecules 28 in the liquid crystal layer 27 are formed to have ahorizontal orientation, a vertical orientation, or a hybrid orientation.The pixel electrodes 22 in the LCoS spatial light modulator 2 are formedof aluminum and function as mirrors for reflecting incident light. Eachpixel electrode 22 corresponds to one pixel when performing phasemodulation.

In the present embodiment, it will be assumed that the LCoS spatiallight modulator 2 has a total of T pixels, where T is a natural number.Each pixel has a unique voltage-dependent phase modulationcharacteristic and a unique voltage-independent phase modulationcharacteristic. Thus, the LCoS spatial light modulator 2 in the presentembodiment satisfies equations (1) and (2). Assuming that a pixelposition in the x and y direction is given by (x, y), Δn(V) is thebirefringence index for the polarization component whose electric fieldthat oscillates in a direction parallel to the liquid crystalorientation, and d(x, y) is the thickness of the liquid crystal layer 27at position (x, y). As will be described later with reference to FIG. 6,each pixel can operate within a voltage range P-S, but in the preferredembodiment is controlled to operate within a prescribed working voltagerange Q-R set within the voltage range P-S.

The circuit for controlling the voltages applied to the pixel electrodes22 is an active matrix circuit, for example. The active matrix circuitincludes transistors and capacitors for each pixel electrode 22.Connected to the transistors are gate signal lines extending in the rowdirection (x direction) for selecting a pixel electrode 22, and datasignal lines extending in the column direction (y direction) forsupplying an analog voltage signal. Pixel electrodes 22 are selected byapplying a Hi signal to the corresponding gate signal line, and thevoltage of the corresponding pixel electrode is controlled by inputtingan analog voltage signal in the capacitor of the selected pixelelectrode 22 through the data signal line. By sequentially switching theselected data and gate signal lines, it is possible to input prescribedvoltages for all pixel electrodes 22.

As shown in FIGS. 4(A)-4(C), a desired voltage is applied to the pixelelectrodes 22 to rotate the corresponding liquid crystal molecules 28.FIG. 4(A) shows the state of the liquid crystal molecules 28 when nopotential difference exists between the pixel electrodes 22 andelectrode 24. FIG. 4(B) shows the state of the liquid crystal molecules28 when a relatively small potential difference exists, and FIG. 4(C)shows the state of the liquid crystal molecules 28 when a relativelylarge potential difference exists. When an applied voltage varies, thebirefringence index in the polarization direction is changed. Thus, thephase of an incident light is modulated.

Linearly polarized light whose polarization plane is parallel to theorientation of the liquid crystal is irradiated from the glass substrate25 side of the LCoS spatial light modulator 2 to modulate the phase ofthe light. Light incident on the glass substrate 25 side propagatesthrough the liquid crystal layer 27 and is reflected by the pixelelectrodes 22, the light again propagates through the liquid crystallayer 27 and is emitted from the glass substrate 25. The phase of thelight is modulated while propagating through the liquid crystal layer27. The light phase distribution can be controlled by modulating thephase of light for each pixel electrode 22. Hence, the LCoS spatiallight modulator 2 can control the wavefront.

As shown in FIG. 2, the control unit 4 is a personal computer, forexample, having a central processing unit (CPU) 41, a communication unit42, a memory unit 43, and a hard disk drive (HDD) 44. The HDD 44 storesa desired pattern 13, look-up tables (LUTs) 11 (sets of reference data)for all T pixels, and a calibration pattern 12. The LUTs 11 have aone-on-one correspondence with each pixel in the LCoS spatial lightmodulator 2 and function to calibrate the voltage-dependent phasemodulation characteristics for the corresponding pixels. The CPU 41functions to control the entire control unit 4. The HDD 44 also stores aprogram for implementing the processing flowchart of FIG. 7 describedlater. The CPU 41 reads this program from the HDD 44 and executes theprogram, enabling the LCoS phase modulator 1 to perform the phasemodulation process shown in FIG. 7.

The desired pattern 13 includes position data for each pixel and a valueindicating a desired phase modulation amount to attain in each pixel(hereinafter referred to as pixel input value). The pixel input value isa digital signal having one of a total of N different input levels (from0 to N−1). In the preferred embodiment, N=256. The N levels of pixelinput values from 0 to N−1 represent phase modulation amounts for oneperiod from 0 to 2π.

The calibration pattern 12 functions to correct voltage-independentdistortion. The calibration pattern 12 includes position data for eachpixel and a value to be added to the pixel input value for each pixel(hereinafter referred to as pixel correction value). The pixelcorrection value is also a digital signal having one of N differentlevels (from 0 to N−1). The pixel correction values for the N levelsfrom 0 to N−1 indicate phase correction amounts for one period from 0 to2π.

The CPU 41 includes a converter 46, and an input value setting unit 47.The input value setting unit 47 sets a control input value A for eachpixel based on the pixel input value and the pixel correction value. Theconverter 46 converts the control input value A set for each pixel to adigital analog (DA) input value B while referencing the correspondingLUT 11.

When performing phase modulation with the LCoS phase modulator 1described above, the CPU 41 reads the LUT 11, calibration pattern 12,and desired pattern 13 into the memory unit 43 from the HDD 44. Theinput value setting unit 47 adds the pixel input values in the desiredpattern 13 to the pixel correction values in the calibration pattern 12for each pixel and sets the control input values A to the sums. Thecontrol input values A are digital signals having one of N total levels(from 0 to N−1). In the preferred embodiment, N=256. If the resultingsum exceeds N, the input value setting unit 47 performs an additionalprocess to fold back the phase of the control input values A and setsthe control input values A to the result of this process. In otherwords, the control input values A are set to conform to the phasemodulation amounts and to correspond to one period (2π[rad]) of phasemodulation amounts from 0 to N−1. Hence, in the phase fold-back processthe input value setting unit 47 replaces the value of control inputvalues A that are negative or that exceed 255 from the addition processdescribed above with the remainder obtained by dividing the values by256. For example, if the sum is 512, the control input value A is set to0. If the sum is 394, the control input value A is set to 128. In orderto find the remainder of a negative value divided by 256, first theinput value setting unit 47 may find the absolute value of the negativevalue and set the sum described above to the smallest positive valuethat can be added to the absolute value to produce an integer multipleof 256. For example, if the sum is −64, the control input value A is setto 192.

The converter 46 converts the control input values A to DA input valuesB for each pixel based on the corresponding LUT 11. The DA input value Bis a digital signal having a total of M input levels (from 0 to M−1),where M is an integer satisfying the expression M>N. In the preferredembodiment, M=4096. The communication unit 42 outputs the DA inputvalues B and other data to the drive unit 3.

The drive unit 3 includes a communication unit 33, a processing unit 31,and a digital analog (D/A) circuit 32. The communication unit 33 is forreceiving data such as the DA input value from the control unit 4. Theprocessing unit 31 generates a digital control signal including avertical synchronization signal, a horizontal synchronization signal,and the like required for driving the LCoS spatial light modulator 2based on the DA input values B. The processing unit 31 also outputs theDA input values B to the D/A circuit 32. The D/A circuit 32 includes thedrive section 321 mentioned above. The drive section 321 converts, foreach pixel, the DA input values B to voltage values within a prescribedworking voltage range Q-R set within the operable voltage range P-S anddrives each pixel with a drive voltage at the acquired voltage value.

First, the drive section 321 converts, for each pixel, the DA inputvalues B to an analog signal C indicating the working voltage to beapplied to the LCoS spatial light modulator 2. As shown in FIG. 6, theD/A circuit 32 is configured to convert a DA input value B between 0 and4095 to an analog signal C indicating a drive voltage value within theworking voltage range Q-R (from a minimum value Q to a maximum value R).Here, the DA input values B (0-4095) are assigned linearly to theworking voltage range Q-R, and the working voltage range Q-R is aportion of the operating voltage range P-S within which the LCoS spatiallight modulator 2 can operate. Each pixel modulates phase of light by aphase amount corresponding to the drive voltage applied theretoaccording to its own phase modulation characteristic.

The converter 46 converts, for each pixel, the control input value A tothe DA input value B using the LUT 11 set for the each pixel. The drivesection 321 further converts the DA input value B to the analog signal Cindicating voltage value within the working voltage range Q-R, andapplies the voltage to the LCoS spatial light modulator 2.

As shown in FIG. 5, the LUT 11 indicates correlations between valuest_(a) (first values) that can be selected as the control input value Aand values t_(b) (second values) that should be selected as the DA inputvalue B. By using the LUT 11, the values t_(b) to be selected as DAinput values B are set so that the values t_(a) that can be selected asthe control input value A and the voltage-dependent phase modulationamount φ attained by the DA input value B have a linear relationship.

FIG. 5 also shows the relation between control input values (t_(a)) andmeasured phase modulation amounts φ attained by corresponding pixelswhen the drive section 321 converts the value t_(b) selected for the DAinput value B to a corresponding voltage value C and applies a voltageof this value to the pixels. However, LUT 11 does not have datacorresponding the phase modulation amounts φ. As shown in FIG. 5, thevalues t_(a) and the phase modulation amounts φ have a linearrelationship. Moreover, the values t_(b) selected for the DA inputvalues B are set such that the phase modulation amounts φ correspondingto each t_(a) selected for the control input values A are substantiallyequal in all LUTs 11. Specifically, the values t_(b) for the DA inputvalues B are set so that φ=1.5 for t_(a)=0, φ=1.5078 for t_(a)=1, etc.

Hence, if the control input values A are converted to DA input values Busing the corresponding LUTs 11 for each pixel, and the DA input valuesB are further converted to analog signals C for applying a voltage, thephase modulation amount φ obtained for each pixel will be substantiallylinear relative to the control input values A. The LUT 11 may includedata corresponding the phase modulation amount φ.

As shown in FIG. 5, the phase modulation amounts Φ obtained through thisprocess are linear relative to the control input values A, with novariation between pixels.

The LCoS phase modulator 1 having the construction described aboveperforms phase modulation according to the operation shown in FIG. 7. Instep 1 (hereinafter step will be abbreviated as S) shown in FIG. 7, theCPU 41 of the control unit 4 reads the calibration pattern 12 into thememory unit 43 from the HDD 44. At the same time, the CPU 41 performs aparallel process in S2 to read the desired pattern 13 into the memoryunit 43 from the HDD 44. However, the CPU 41 may also create the desiredpattern 13 and save the desired pattern 13 in the memory unit 43 at thistime. In S3 the input value setting unit 47 adds the pixel input valuesin the desired pattern 13 to the pixel correction values in thecalibration pattern 12 for each pixel, folding back the phase for sumswhen necessary, to find the control input value A for each pixel. In S4the CPU 41 reads the LUTs 11 corresponding to each pixel into the memoryunit 43 from the HDD 44. In S5 the converter 46 finds the DA input valueB for the control input value A of each pixel by referencing thecorresponding LUT 11. In S6 the CPU 41 transmits the DA input values Bto the communication unit 33 in the drive unit 3 via the communicationunit 42. Subsequently, the processing unit 31 receives the DA inputvalue B from the communication unit 33, and transfers the DA inputvalues B to the D/A circuit 32, at which time the processing unit 31produces digital control signals. The drive section 321 converts the DAinput values B to analog signals C and outputs the analog signals C tothe LCoS spatial light modulator 2. At the same time, the digitalcontrol signals are outputted from the processing unit 31 to the LcoSspatial light modulator 2. Accordingly, the LCoS spatial light modulator2 modulates the phase of incident light.

When the LCoS phase modulator 1 is manufactured, the drive section 321,the LUTs 11, and the calibration pattern 12 are set to correspond to theLCoS spatial light modulator 2 provided in the LCoS phase modulator 1.The HDD 44 also stores the program for implementing the processingflowchart of FIG. 7. The order in which the settings are made is asfollows. First, minimum and maximum voltages Q and R are set for theworking voltage range Q-R of the D/A circuit 32. Next, an LUT 11 is setfor each pixel, after which the calibration pattern 12 is created.Finally, the HDD 44 stores the program for implementing the processingflowchart of FIG. 7.

The method of setting the minimum value Q and maximum value R for theworking voltage will be described with reference to FIG. 8. First, inS11 of FIG. 8 a polarization interferometer 60 shown in FIG. 9 is usedto measure voltage-dependent phase modulation characteristics (φ) for aplurality (five for example) of arbitrarily selected pixels. As shown inFIG. 9, the polarization interferometer 60 is configured of a Xenon lamp61, a collimator lens 62, a polarizer 63, a beam splitter 64, the LCoSphase modulator 1, an analyzer 65, image lenses 66 and 67, a band passfilter 68, and an image sensor 69. In S11, the drive section 321 isinitially set to assign DA input values B (0-4095) for the entire partof the operating voltage range P-S of voltages that can be applied tothe LCoS spatial light modulator 2, as shown in FIG. 10. The drivesection 321 of the D/A circuit 32 converts the same DA input value B tothe analog signal C for all pixels and drives the LCoS spatial lightmodulator 2 with the same analog signals C, while the polarizationinterferometer 60 measures the phase modulation amounts. Themeasurements are repeated for each DA input value B from 0 to 4095. Theimage sensor 69 measures light that has been phase-modulated with theLCoS spatial light modulator 2. Since the polarizing direction of thepolarizer 63 is shifted 45° from the orientation of liquid crystalmolecules in the LCoS spatial light modulator 2, light incident on theLCoS spatial light modulator 2 (incident light) is shifted 45° to theorientation of the liquid crystal molecules 28. The incident lightpasses through the liquid crystal layer 27, producing a phase differencebetween the component in which the incident light is phase-modulated(component parallel to the orientation of the liquid crystal molecules28) and the component not phase-modulated. Hence, the polarizingdirection of light reflected by the LCoS spatial light modulator 2(reflected light) is dependent on the phase modulation amount of thephase-modulated component in the incident light. Further, theorientation of the analyzer 65 is shifted 90° relative to the polarizer63. The intensity of light passing through the analyzer 65 is dependenton the polarizing direction of the reflected light. Thus, the imagesensor 69 measures voltage-dependent phase modulation characteristics asintensity data I. The phase modulation amount φ for a certain pixel canbe found from the intensity data I measured by the image sensor 69according to the following equation, for example.

φ=2 sin⁻¹(((I−I _(min))/(I _(max) −I _(min)))^(1/2))

Here, I_(max) is the maximum value of intensity data measured whilevarying the voltage applied to the same pixel within the operatingvoltage range, and I_(min) is the minimum value of such intensity data.

In S12 the CPU 41 finds the DA input value-voltage-dependent phasemodulation characteristics for each pixel based on the results ofmeasurements with the image sensor 69. FIG. 10 is a graph showing therelationship between the DA input values and voltage-dependent phasemodulation amount obtained for five pixels. The graph in FIG. 10confirms the following points (A)-(D). (A) The phase modulation amountsexceed 2π[rad]. (B) A region exists in which the phase modulation amountchanges very little despite a change in voltage (the range of DA inputvalues 0-800). The upper limit of this range will be referred to as athreshold voltage. (C) The phase modulation amounts differ among thefive pixels. (D) The phase modulation amounts are nonlinear relative tothe DA input values.

If the LcoS spatial light modulator 2 can achieve the phase modulationamounts in a range 0-2π[rad] or a range such that difference between amaximum value of the range and a minimum value of the range is 2π[rad],it is possible to obtain phase modulation amounts greater than 2π[rad]by performing the phase fold-back process. Hence, the range of drivevoltages applied to the liquid crystal is sufficient, provided that a2π[rad] range of phase modulation amounts can be ensured. However, whenactually correcting distortion, it is necessary to have a certain degreeof excess (margin) of the phase modulation amount to account forirregularities in the phase modulation amount for each pixel. Therefore,the range of drive voltages should be set to a value capable ofachieving a phase modulation amount greater than 2π[rad]. In thepreferred embodiment, this value is set to 3.5π[rad], that is, the rangeof drive voltages is set to achieve a phase modulation amount of3.5π[rad]. Here, the phase fold-back process is similar to the processfor folding back the phase of control input values. In other words, ifthe phase is greater than or equal to 2π[rad] or smaller than 0, thephase is replaced with a reminder value obtained by dividing the phaseby 2π[rad].

More specifically, in S13 the minimum value Q of the working voltageapplied to the LCoS spatial light modulator 2 is set greater than orequal to the threshold voltage at which the liquid crystal starts tooperate, the maximum value R is set less than or equal to a saturationvoltage at which operation of the liquid crystal is saturated, and thephase modulation range between the minimum value Q and maximum value Rof the working voltage is set to approximately 3.5π. In this way, the DAinput values B are associated with 4096 levels for the region betweenthe minimum value Q and maximum value R of the working voltage. FIG. 11shows the relationship between the DA input values B, the phasemodulation amount, and the working voltage range Q-R when the minimumvalue Q and maximum value R are set according to the above conditions.When using the entire operable voltage range of the LCoS spatial lightmodulator 2 in the example of FIG. 10, the DA input values haveapproximately 700 levels between about 1100 and 1800 for the range ofphase modulation amounts from 0.5π to 4π[rad]. In the example of FIG.11, the voltage can be controlled at 4096 levels for the same range ofphase modulation amounts (0.5π-4π[rad]). In other words, the DA inputvalues have about five times the number of levels for the same range ofphase modulation amounts, thereby enabling the voltage to be controlledwith great accuracy. Hence, by setting the minimum and maximum voltagesQ and R, it is possible to convert the scale of the working voltagerange for the DA input values. The drive section 321 is configured toconvert the DA input values 0-4095 linearly to analog signals C, whichspecify voltage values in the working voltage range Q-R. The minimum andmaximum voltages Q and R are set to the same values for all pixels.

Next, a method of creating the LUT 11 will be described with referenceto FIG. 12. The creating LUT 11 process is performed after setting theworking voltage Q-R. The LUT 11 is created for each pixel aftercompleting the settings for the drive section 321. In S21, using thepolarization interferometer 60 shown in FIG. 9, the relationship of theDA input values B and the voltage-dependent phase modulation amounts isobtained for each pixel in the LCoS spatial light modulator 2.Specifically, the polarization interferometer 60 measures the phasemodulation amount for each pixel obtained when the same DA input value Bis inputted for all pixels. Hence, the drive section 321 of the D/Acircuit 32 converts the same DA input value B to the same analog signalC for all pixels and drives the LCoS spatial light modulator 2 with theanalog signals C, while the polarization interferometer 60 measures thephase modulation amounts. The measurements are repeated for each DAinput value B from 0 to 4095. In S22 the CPU 41 finds the DA inputvalue-voltage-dependent phase modulation characteristics for each pixelbased on the measured values found in S21. The results are similar tothose in FIG. 11 described above, showing nonlinearity between thecontrol input value and the phase modulation amount with irregularityamong pixels.

In S23 the CPU 41 creates an LUT 11 for each pixel based on the DA inputvalue-voltage-dependent phase modulation characteristics found above.Specifically, using the least-squares method or the like, therelationship between the DA input value and phase modulation amount isapproximated with a polynomial expression using the phase modulationamount as a variable. This relationship is obtained for each pixel. Thisapproximation can reduce the effects of measurement noise caused by thelight source, image sensor, and the like. In S21 it is also possible toperform measurements for intervals of DA input values B rather than forall DA input values B and to estimate data for the DA input values B notused in measurements with this approximation. The approximationexpresses the DA input value t_(b) as a K-th polynomial of the phasemodulation amount φ as in the following equation.

$\begin{matrix}{t_{b{(1)}} = {{f_{1}(\varphi)} = {\sum\limits_{{k{(1)}} = 0}^{K}{a_{k{(1)}}\varphi^{k{(1)}}}}}} & (3)\end{matrix}$

In the above equation, the index (1) represents a value in theapproximating polynomial found based on the first measurement. In thisway, an approximation indicating the relationship between the DA inputvalue and the phase modulation amount is found for each pixel. However,in order to represent 0.0-2.0π[rad] as 256 levels of control inputvalues A and the relationship between the control input value A and thephase modulation amount is linear, the relationship of control inputvalue A with the phase modulation amount φ is expressed by the followingequation, where t_(a(1)) indicates the control input value A.

φ(t _(a(1)))=(2π/256)×t _(a(1)) +const  (4)

Here, t_(a(1)) is an integer from 0 to 255, and const is an offsetvalue. The offset value is set to the same value capable of realizingequation (4) for all pixels. The relationship between the control inputvalue t_(a(1)) and t_(b) is found by substituting equation (4) intoequation (3). Since t_(b) is an integer, it is necessary to round off(or round out/down) to the nearest integer. Hence, the relationshipbetween t_(a(1)) and t_(b) is expressed by the following equation, whereROUND represents the rounding off operation.

t _(b)=ROUND└f ₁(φ(t _(a(1))))┘  (5)

The LUT 11 is created by associating values of t_(b(1)) found inequation (5) for values 0-255 of t_(a(1)).

In S24 the CPU 41 saves the LUTs 11 created above in the HDD 44. Theabove LUTs 11 are obtained by calculating the phase from intensityoutput from the interferometer. While the minimum and maximum values ofthe measured interference intensity are used to create the LUT 11, thereis potential for these values to contain errors. In S25-S27, the degreeof error in these values is evaluated.

Specifically, in S25 the relationship between the control input valuest_(a) and the phase modulation amount φ is measured for all pixels, asdescribed in S21. However, in S25 the converter 46 first converts thecontrol input values A to DA input values B based on the LUTs 11 foreach pixel just obtained in S24, after which the drive section 321converts the DA input values B to analog signals C and drives thecorresponding pixels in the LCoS spatial light modulator 2 based on theanalog signals C. Through this process, the relationship between thecontrol input values A (t_(a)) and the voltage-dependent phasemodulation amount φ is measured for all pixels. In S26 the CPU 41 findsthe control input value-phase modulation characteristics based on theresults in S25. In S27 the CPU 41 determines from the results in S26whether the LUTs 11 corrected the voltage-dependent phase modulationcharacteristics with the desired precision. For example, the CPU 41 maydetermine that the desired precision was obtained if the control inputvalue-voltage-dependent phase modulation characteristics approachlinearity, but the method of determination is not limited to thisexample. If the CPU 41 determines that the desired precision was notattained in S27, then the CPU 41 returns to S23 and updates the LUTs 11based on the results in S26 to improve the precision for correcting thevoltage-dependent phase modulation characteristics with the LUTs 11.

When executing S23 for the second time, the CPU 41 approximates therelationship between the control input values A (t_(a)) and the phasemodulation amount φ according to the following equation, where M is anatural number greater than or equal to 2.

$\begin{matrix}{t_{a{({M - 1})}} = {{f_{M}(\varphi)} = {\sum\limits_{{k{(M)}} = 0}^{K}{a_{k{(M)}}\varphi^{k{(M)}}}}}} & (6)\end{matrix}$

Here, M represents a number of time to execute S23. When executing S23for the second time (M=2), the equation (6) becomes as followingexpression.

$t_{a{(1)}} = {{f_{2}(\varphi)} = {\sum\limits_{{k{(2)}} = 0}^{K}{a_{k{(2)}}\varphi^{k{(2)}}}}}$

As in the case of the equation (4), the control input values must have alinear relationship with the phase modulation amount. Thus, followingequation must be satisfied.

φ(t _(a(M)))=(2π/256)×t _(a(M)) +const  (7)

Here, t_(a(M)) represents a control input values that is expressed in256 levels.

Based on equations (6) and (7), the relationship between the previouscontrol input values A (t_(a(1))) and the current control input values A(t_(a(2))) can be expressed as follows.

t _(a(M-1)) =f _(M)(φ(t _(a(M))))  (8)

The relationship between t_(b) and t_(a(2)) is expressed as follows bysubstituting equation (8) into equation (5).

t _(b)=ROUND└f ₁(φ(f ₂(φ(t _(a(2))))))┘  (9)

Equation (9) is used to find the relationship between the new controlinput values A (t_(a(2))) and the DA input value B (t_(b)). If the CPU41 executes S23 J times (where J is a natural number such that J>2), theCPU 41 finds the following relationship for t_(b) and t_(a(J)).

t _(b)=ROUND└f ₁(φ(f ₂( . . . f _(J)(φ(t _(a(J))))))┘  (10)

Here, the equations (6)-(8) are obtained for every time when returningto and executing S23. That is, the equations (6)-(8) are obtained forall M from 2 to J. Thus, the equation (10) is acquired from theseequations (6)-(8) for all M from 2 to J.

In S23 the CPU 41 creates new LUTs 11 based on these values, and in S24overwrites the LUTs 11 in the HDD 44 with the new LUTs 11. However, whenthe CPU 41 determines that the desired precision is obtained in S27 orwhen the CPU 41 determines that an improvement in precision is notobtained with the new LUTs 11 over the previous LUTs 11, the CPU 41 endsthe LUT creating process.

The table in FIG. 5 shows the relationship between the t_(a), t_(b), andphase modulation amounts φ obtained in the above process for a certainpixel. A linear relationship of high precision is achieved between thecontrol input values and the phase modulation amounts through conversionwith the LUT 11.

The graph in FIG. 13 shows the relationship between the control inputvalues A and the voltage-dependent phase modulation amounts for eachpixel of the LCoS spatial light modulator 2 when phase modulation isperformed using the corresponding LUTs 11. The dotted line indicates anideal linear relationship between the control input values A and thephase modulation amounts. The bold line indicates the relationshipbetween the control input values A and the phase modulation amounts forpixels having values closest to the dotted line, while the normal lineindicates the relationship between the control input values A and thephase modulation amounts for pixels having values furthest from thedotted line. As can be seen, calibration performed using the LUTs 11according to the preferred embodiment correct irregularities in phasemodulation amounts among the pixels to achieve a linear relationshipbetween the control input values A and the phase modulation amounts.

After creating an LUT 11 for each pixel in the above process, the CPU 41creates the calibration pattern 12. While voltage-independent distortionnormally cannot be measured separately from the voltage-dependent phasemodulation amount, this distortion can be measured by measuring theoutput wavefront of the LCoS phase modulator 1 when thevoltage-dependent phase modulation characteristics have been correctedusing the LUTs 11. The wavefront of light containing voltage-independentdistortion is measured using a two-beam interferometer. In the preferredembodiment, a Michelson interferometer 80 shown in FIG. 14 is used asthe two-beam interferometer. The Michelson interferometer 80 isconfigured of a laser light source 81, a spatial filter 82, a collimatorlens 83, a polarizer 84, a beam splitter 85, the LCoS phase modulator 1,a mirror 86, image lenses 87 and 88, and a CCD 89. The polarizingdirection of the polarizer 84 is parallel to the orientation of theliquid crystal. The Michelson interferometer 80 measures a fringepattern produced by interference between a wavefront reflected off themirror 86 and a wavefront reflected off the LCoS spatial light modulator2 in the LCoS phase modulator 1. Using the method of fringe patternanalysis described in “Fourier-transform method of fringe patternanalysis for computer-based topography and interferometry”, M. Takeda,H. Ina, and S. Kobayashi, J. Opt. Soc. Am., Vol. 72, 156-160 (1982), itis possible to find the output wavefront of the LCoS phase modulator 1from the measured fringe pattern. That is, a voltage-independentdistortion pattern is formed in the wavefront reflected by the LCoSspatial light modulator 2, and the wavefront reflected by the mirror 86is a plane wave. Accordingly, the voltage-independent distortion can beobtained by taking the Fourier transform of the fringe pattern andremoving the carrier component.

Next, a method of creating the calibration pattern 12 for correctingvoltage-independent distortion will be described with reference to FIG.15. In S31 the CPU 41 initializes the calibration pattern 12 to apattern in which the value of all pixels is 0. In S32 the CPU 41 setsthe desired pattern 13 to a phase image in which the control inputvalues A for all pixels are equivalent for any value from 0 to 255. InS33 the input value setting unit 47 adds the pixel input values in thedesired pattern 13 to the pixel correction values in the calibrationpattern 12 for each pixel and sets the control input values A to theresults after performing the phase fold-back process. In S34 theconverter 46 converts the control input values A to DA input values Bbased on the LUTs 11 corresponding to each pixel and transfers the DAinput values B to the drive unit 3. In S35 the drive section 321generates analog signals C based on the DA input values B in order toapply working voltages to the LCoS spatial light modulator 2. In S36 theCPU 41 measures the output wavefront of the LCoS phase modulator 1 basedon results outputted from the CCD 89 of the Michelson interferometer 80.Since the voltage-dependent phase modulation characteristics have beencorrected with the LUTs 11, the wavefront measured in S36 includes onlyvoltage-independent distortion. In S37 the CPU 41 creates a pattern inwhich the signs of the measured voltage-independent distortion arereversed. In S38 the CPU 41 performs a phase fold-back process on phasevalues in the pattern acquired in S37. In S39 the CPU 41 references theLUTs 11 to represent the phase value of each pixel in the pattern as oneof 256 levels after the pattern has undergone the phase fold-backprocess and converts the levels to control input values to obtain thecalibration pattern 12. This conversion is achieved, for example, byusing equation (4) or (7) that represents an ideal relation between thephase modulation amounts and the control input values. It may alsopossible to store the relation between the measured phase modulationamounts and the control input values in the LUTs 11 as shown in FIG. 5and to achieve the conversion by using these LUTs 11. FIG. 16 shows anexample in which the calibration pattern 12 is rendered as an image in256 levels. In S40 the CPU 41 saves the calibration pattern 12 in theHDD 44.

As when creating the LUTs 11, measures of interference may containerrors in the process described above. The degree of these errors isanalyzed in S41-S45. Specifically, as in S33 described above, in S41 theinput value setting unit 47 adds the pixel input values in the desiredpattern 13 described above to the pixel correction values in thecalibration pattern 12 just obtained in S40, setting the results as thecontrol input values A and performing phase fold-back on the controlinput values A when necessary. Steps S42-S44 are identical to S34-S36.In S42 the converter 46 finds DA input values B corresponding to thecontrol input values A obtained in S41. In S43 the drive section 321converts the DA input values B to analog signals C for applying drivevoltage to the LCoS spatial light modulator 2. In S44 the CPU 41measures the output wavefront based on the results outputted from theCCD 89. In S45 the CPU 41 determines based on the results of thesemeasurements whether the calibration pattern 12 just obtained in S40 isable to perform correction at the required precision. For example, theCPU 41 may determine that the desired precision is obtained if thewavefront has a desired flatness, but the determination method is notlimited to this example. The CPU 41 ends the calibration patterncreating process upon determining in S45 that the calibration pattern 12obtained the required precision or an improvement in precision is notobtained over the previous calibration pattern 12. If the requiredprecision was not obtained, the CPU 41 returns to S37 and recreates thecalibration pattern 12 based on the voltage-independent distortionindicated in the results from S44. Specifically, in S40 the CPU 41 addsthe pixel correction values from the calibration pattern 12 obtainedpreviously to the pixel correction values from the calibration pattern12 just obtained for each pixel and saves the sums in the HDD 44. Inother words, to obtain a new calibration pattern 12, the CPU 41 adds thepixel correction values for the calibration pattern 12 currentlyobtained in S39 and the pixel correction values for the calibrationpattern 12 previously obtained in S39 for each pixel. In this way, theCPU 41 repeatedly updates the calibration pattern 12.

The LCoS phase modulator 1 according to the preferred embodimentdescribed above controls the LCoS spatial light modulator 2 for DA inputvalues B expressed in 4,096 levels within the working voltage rangesmaller than the operable voltage range that ensures the required rangeof the phase modulation amounts. Hence, the LCoS phase modulator 1 cancontrol the voltages applied to the LCoS spatial light modulator 2 withgreat accuracy. Moreover, the LCoS phase modulator 1 employs the LUTs 11to achieve a substantially linear relationship between the control inputvalues A and the voltage-dependent phase modulation amounts and correctsirregularities among pixels caused by voltage dependence, therebyobtaining the desired phase modulation amounts with great accuracy.Further, the LCoS phase modulator 1 uses the calibration pattern 12 tocorrect voltage-independent distortion to achieve more accurate phasemodulation. FIG. 17(A) shows measurements of phase modulation for aLaguerre-Gaussian beam using the LUTs 11 and the calibration pattern 12.FIG. 17(B) shows the same beam when corrections are not performed. Asexpected, a pattern of concentric circles can be seen in FIG. 17(A).

Further, when creating the LUTs 11 and when creating the calibrationpattern 12, the process is repeated until either the required precisionis obtained or until an improvement in precision is not obtained. Thus,it is possible to obtain highly accurate LUTs 11 and a highly accuratecalibration pattern 12 capable of accurately correctingvoltage-dependent phase modulation characteristics andvoltage-independent distortion.

First Variation of the First Embodiment

While the pixel electrodes 22 also function as mirrors in the LCoSspatial light modulator 2 described above, a device such as a LCoSspatial light modulator 120 shown in FIG. 18 having a dielectric mirror29 layered over the pixel electrodes 22 may be used in place of the LCoSspatial light modulator 2. Here, parts and components of the LCoSspatial light modulator 120 similar to those in the LCoS spatial lightmodulator 2 have been designated with the same reference numerals toavoid duplicating description.

Second Variation of the First Embodiment

While the LUTs 11 and the calibration pattern 12 are stored in the HDD44 on the control unit 4 in the LCoS phase modulator 1 according to thefirst embodiment, the LUTs 11 may be saved in a drive unit 130 insteadof the HDD 44, as in an LCoS phase modulator 100 shown in FIG. 19.Specifically, the control unit 4 does not store the LUTs 11 in the HDD44. Further, the CPU 41 is not provided with the converter 46, ratherthe drive unit 130 has an LUT processor 135 that functions as aconverter. More specifically, the drive unit 130 includes a processingunit 131, a D/A circuit 132, a communication unit 133, a RAM 134 forsaving the LUTs 11, and the LUT processor 135. The LUTs 11 are saved inROM (not shown) in the drive unit 130 and read into the RAM 134 when theLCoS phase modulator 100 is started. The structure of the LCoS spatiallight modulator 2 is identical to that in the LCoS phase modulator 1 ofthe first embodiment. Further, the structures of the communication unit133 and D/A circuit 132 are identical to the communication unit 33 anddigital analog (D/A) circuit 32 shown in FIG. 2.

For phase modulation, the input value setting unit 47 sets the controlinput values A for each pixel by adding the desired pattern 13 andcalibration pattern 12 and transmits the control input values A to thedrive unit 130. The control input values A are transferred to the LUTprocessor 135 via the communication unit 133 and processing unit 131.The LUT processor 135 converts the control input values A to DA inputvalues B based on the LUTs 11 in the RAM 134. The LUT processor 135transfers the DA input values B to the D/A circuit 132, which convertsthe DA input values B to analog signals C indicating operating voltagevalues for driving the LCoS spatial light modulator 2.

Third Variation of the First Embodiment

The drive unit 3 may also be replaced with a drive unit 230 that holdsthe LUTs 11 and calibration pattern 12, as in an LCoS phase modulator200 shown in FIG. 20. In this example, the CPU 41 is provided withneither the converter 46 nor the input value setting unit 47. Insteadthe drive unit 230 has an adder 235 function as the input setting unit47 and an LUT processor 236 that functions as a converter. Further, thecalibration pattern 12 and LUTs 11 are not stored in the HDD 44. Morespecifically, the drive unit 230 has a processing unit 231, a D/Acircuit 232, a communication unit 233, a RAM 234 for holding the LUTs 11and the calibration pattern 12, an adder 235, and the LUT processor 236.The LUTs 11 and the calibration pattern 12 are saved in ROM (not shown)on the drive unit 230 and are read into the RAM 234 when the LCoS phasemodulator 200 is started. The structures of the communication unit 233and D/A circuit 232 are identical to the communication unit 33 and D/Acircuit 32 in FIG. 2. When the control unit 4 transmits pixel inputvalues indicating a desired pattern to the drive unit 230, the adder 235adds the calibration pattern 12 in the RAM 234 to the pixel input valuesto produce the control input values A and transmits the control inputvalues A to the LUT processor 236. The LUT processor 236 converts thecontrol input values A to DA input values B by referencing the LUTs 11and transmits the DA input values B to the D/A circuit 232. In the D/Acircuit 232, the drive section 321 converts the DA input values B toanalog signals C indicating the operating voltages and outputs theanalog signals C to the LCoS spatial light modulator 2.

The functions of the control unit 4 may also be incorporated in thedrive unit 230. In this case the RAM 234 also stores the desired pattern13. Both the desired pattern 13 and the calibration pattern 12 are savedin ROM (not shown) in the drive unit 230 and read into the RAM 234 whenthe LCoS phase modulator 200 is started.

Fourth Variation of the First Embodiment

While the drive unit 3 shown in FIG. 2 is provided with only one D/Acircuit 32, the drive unit 3 may be given a plurality of D/A circuits 32for simultaneously outputting a plurality of analog signals to the LCoSspatial light modulator 2 in order to simultaneously write analogsignals to a plurality of pixels. In the drive unit 3 having thisconstruction, the process circuit of the drive unit 3 is configured tosimultaneously output DA input values B for a plurality of pixels to theD/A circuits 32.

Fifth Variation of the First Embodiment

While an LUT 11 is created for each pixel in the first embodimentdescribed above, it is possible to form blocks, each of which includes aplurality of neighboring pixels, and to create one LUT 11 for eachblock. For example, a single block may be configured of 2×2 pixels or4×4 pixels, with one LUT 11 created for each block. Here, thevoltage-dependent phase modulation characteristics for at least onepixel in a block are measured, and the LUT 11 is created for the blockbased on the average of measured values for the at least one pixel inthe block. However, when the voltage-dependent phase modulation amountis measured for only one pixel in the block, the LUT 11 may be createdbased simply on the measured value of the pixel rather than an averagevalue. This configuration can reduce the amount of data stored for theLUTs 11, since it is not necessary to prepare an LUT 11 for each pixel.

It is also possible to vary the number of pixels constituting a block.In this case, an LUT 11 is created for each block based on the controlinput value-voltage-dependent phase modulation characteristics for thecorresponding block. Since the phase modulation amount varies accordingto the thickness of the liquid crystal layer, the number of pixelsconstituting a block may be reduced in areas where the liquid crystallayer thickness changes greatly (for example, setting a block equivalentto one pixel) and increased in areas where changes in liquid crystallayer thickness are slight (for example, setting a block equivalent to8×8 pixels). With this configuration, correction can be performedaccurately and efficiently, while reducing the amount of data saved forthe LUTs 11.

Sixth Variation of the First Embodiment

The calibration pattern 12 may also be configured to hold values forunits of blocks. In this case, the phase modulation characteristics aremeasured for at least one pixel in a block, and the correction value foreach pixel in the block is set to the average value of correction valuesfor each pixel that were found in the block. However, when the phasemodulation characteristics are measured for only one pixel in a block,the correction value for the block may be simply set to the correctionvalue for that pixel rather than an average value.

Seventh Variation of the First Embodiment

Further, as shown in FIG. 21, the values of the calibration pattern 12may be included in the LUTs 11. Here, for a given pixel, t representsthe pixel input value of the desired pattern 13 and p represents thepixel correction value of the calibration pattern 12. In the preferredembodiment, after setting the control input value A by adding the pixelinput value t to the pixel correction value p, the control input value Ais converted to the DA input value by applying the LUT 11. That is, whenreferencing the LUT 11, the value t+p is the reference position of thecontrol input value A. The desired image is changed as needed, that is,the pixel input value t varies depending on the desired pattern 13.However, the pixel correction value p is a fixed value. Hence, thereference position is always shifted from the input value t by the valuep. This is equivalent to shifting the reference start position in theLUT by the value p.

Hence, data for correcting voltage-independent distortion can beincluded in the LUT 11 by shifting the reference position in the LUT 11for each pixel by the value in the calibration pattern for the samepixel. FIG. 21 has included data for correcting voltage-independentdistortion as well as the data of FIG. 5, with p=128. For example, thevalue of t_(b) is 1,030 when t_(a) is 0 in the table of FIG. 5, but thisvalue of t_(b) appears when t_(a) is 128 in FIG. 21.

Here, additional examples will be described for the cases when p=1 andp=−1. In the LUT 11 shown in FIG. 5, the DA input values t_(b)corresponding to control input values t_(a) 255, 0, and 1 are 3,036,1,030, and 1,035, respectively. When p=1, it is possible to create anLUT 11 that associates DA input values t_(b) of 1,030, 1,035, and 1,056with the same control input values t_(a) of 255, 0, and 1.Alternatively, when p=−1, it is possible to create an LUT 11 thatassociates DA input values t_(b) of 3,028, 3,036, and 1,030 with thesame control input values t_(a).

In this case, steps S1 and S3 are not required in the phase modulationmethod described with reference to FIG. 7. In S1 of FIG. 7, the CPU 41reads the desired pattern 13, and the input value setting unit 47 setsthe value of each pixel in the desired pattern 13 as an control inputvalue A. In S4 the CPU 41 reads the LUT 11 in FIG. 21 for each pixel. InS5 the converter 46 converts the control input values A to DA inputvalues B by referencing the LUTs 11 in FIG. 21 for each pixel. Hence,the control unit 4 can also correct voltage-independent distortionsimply by applying the LUTs 11 that include the calibration pattern,thereby eliminating the need to save the calibration pattern and toperform a process to add the calibration pattern to the desired image.

The LUTs 11 including the calibration pattern can also be created byunits of blocks. In this case, the LUTs 11 and the calibration pattern12 are divided into blocks according to the same method described above.More specifically, the size and position of the blocks in the LUTs 11and the calibration pattern 12 are identical to each other. The valuefor each block in the calibration pattern 12 is simply reflected in thecorresponding block constituting the LUTs 11.

In this way, data in the calibration pattern 12 can be included in theLUTs 11 for correcting voltage-independent distortion while the LUTs 11are used to convert control input values A to DA input values B.Therefore, the process of adding the calibration pattern 12 may beomitted, achieving more efficient phase modulation.

Eighth Variation of the First Embodiment

While the D/A circuit 32 is provided in the drive unit 3 in the firstembodiment described above, the D/A circuit may be separated from thedrive unit 3, and the LCoS spatial light modulator 2 may be providedwith the D/A circuit and a new reception circuit for receiving the DAinput values B. With this construction, the drive unit 3 transfers theDA input values B to the reception circuit on the LCoS side.

Ninth Variation of the First Embodiment

The D/A circuit 32 may also be replaced with a pulse modulation circuit.With this construction, the pulse modulation circuit outputs a digitalpulse modulation signal for driving the LCoS spatial modulator.

Tenth Variation of the First Embodiment

In the first embodiment described above, the voltage-dependent phasemodulation characteristics are measured for five pixels, and the minimumand maximum voltages Q and R are set based on the measurement results.However, provided that at least one pixel is measured, the number ofmeasured pixels is arbitrary, and the minimum and maximum voltages areset based on the voltage-dependent phase modulation characteristics ofthe measured at least one pixel.

Eleventh Variation of the First Embodiment

Further, it is possible to save data for the approximating polynomialsfound in equations (3), (4) and (6) (coefficients a_(k(I)), where 1≦I≦J,and value “const”), as sets of reference data, in the HDD 44 instead ofthe LUTs 11 and to convert control input values A to DA input values Bbased on this data when measuring the phase modulation amount. Hence, asin the method of creating the LUTs 11 in the first embodiment (S23), therelationship between the control input values A and DA input values Bcan be obtained from the data stored in the HDD 44 and equations (4) and(7) by getting equations (5), (9) or (10), depending on a number of timeto return to S23. Other various types of sets of reference data can beemployed instead of the LUTs 11 ore the coefficients for theapproximating polynomials.

Second Embodiment

Next, a second embodiment of the present invention will be describedwith reference to FIGS. 22 through 29. In the first embodiment describedabove, the LUT 11 is prepared for each pixel to calibrate thevoltage-dependent phase modulation characteristics of that pixel. In thesecond embodiment, a plurality of pixels having similarvoltage-dependent phase modulation characteristics are combined in agroup, and an LUT 51 is prepared for each group.

As shown in FIG. 22, an LCoS phase modulator 500 according to thepresent embodiment includes the LCoS spatial light modulator 2, a driveunit 530 for driving the LCoS spatial light modulator 2 with voltage,and the control unit 4. Parts and components similar to the firstembodiment described above have been designated with the same referencenumerals to avoid duplicating description.

In the second embodiment, the total of T pixels are divided into rgroups based on their voltage-dependent phase modulationcharacteristics. (Here, T and r are positive integers satisfying theexpressions T>0, r>0, and T>r. In the preferred embodiment, r is 20.)Hence, each group includes pixels having similar phase modulationcharacteristics.

As shown in FIG. 22, the control unit 4 has the same construction as thecontrol unit 4 in the first embodiment, but the HDD 44 does not storethe LUTs 11 or calibration pattern 12, but stores only the desiredpattern 13.

When phase modulation is performed with the LCoS phase modulator 500,the CPU 41 reads the desired pattern 13 into the memory unit 43 from theHDD 44. The CPU 41 transmits the desired pattern 13 as input data to thedrive unit 530 via the communication unit 42. The input data of thedesired pattern 13 includes pixel position data and a pixel input valuefor each pixel. As in the first embodiment, the pixel input value is adigital signal having one of N levels from 0 to N−1.

The drive unit 530 includes a communication unit 533, a processing unit531, an adder 535, an LUT processor 536, a pixel position detector 537,a D/A circuit 532, a RAM 538, and a RAM 539. The D/A circuit 532includes the drive section 321 described in the first embodiment. TheRAM 538 stores the calibration pattern 12. The calibration pattern 12includes a pixel correction value (digital signals having N levels from0 to N−1) and pixel position data for each pixel. The drive unit 530also stores a program for implementing a process, described later, shownin the flowchart of FIG. 27 in a ROM (not shown). The processing unit531 reads this program from the ROM (not shown) and entirely controlsthe LCoS phase modulator 500 by executing the program in the phasemodulation process.

The RAM 539 stores a single LUT map 15, and r number of LUTs 51 (sets ofreference data). The LUT map 15 indicates to which group among the rgroups each pixel belongs. The r LUTs 51 have a one-on-onecorrespondence to the r groups. Each LUT 51 functions to correctvoltage-dependent phase modulation characteristics of pixels belongingto the corresponding group. By correcting the voltage-dependent phasemodulation characteristics of each pixel in a group with the LUT 51corresponding to the group to which the pixels belong, it is possible toconvert nonlinear characteristics to linear characteristics for eachpixel and to correct irregularities in these characteristics among thepixels.

The communication unit 533 receives input data of the desired pattern 13(the pixel input value and the pixel position) and other data from thecontrol unit 4 and transfers this data to the processing unit 531. Theprocessing unit 531 generates a digital control signal including avertical synchronization signal and horizontal synchronization signalrequired for driving the LCoS spatial light modulator 2 based on thedesired pattern 13. At the same time, the processing unit 531 transfersthe desired pattern 13 to the adder 535. Also at the same time, theprocessing unit 531 outputs position data for pixels in the desiredpattern 13 to the pixel position detector 537.

The adder 535 adds the pixel input values in the desired pattern 13 tothe pixel correction values in the calibration pattern 12 for each pixeland sets the control input values A corresponding to these pixels to thesums. If the sums exceed N, the adder 535 also performs a phasefold-back process on the sums and sets the control input values A to theresults. The adder 535 transmits the control input value A for eachpixel together with the position data for the pixel to the LUT processor536.

The pixel position detector 537 references the LUT map 15 and determinesa group number for the group to which each pixel belongs based onposition data for the pixels in the desired pattern 13. The pixelposition detector 537 transfers the position data for each pixel and theLUT 51 corresponding to the specified group number (in other words, theLUT 51 corresponding to the position data of the pixel) to the LUTprocessor 536.

The LUT processor 536 references position data together with theacquired LUT 51 for each pixel and converts the control input value Areceived together with the position data to a DA input value B. Here,the DA input value B is a digital signal having one of a total of Mlevels (from 0 to M−1).

The LUT processor 536 converts, for each pixel, the control input valueA to the DA input value B with the LUT 51, and the drive section 321converts the DA input value B to an analog signal C indicating a voltagevalue within the working voltage range Q-R and applies this voltage tothe LCoS spatial light modulator 2.

The LUT map 15 is created according to a method described later based oncharacteristics of the LCoS spatial light modulator 2 provided in theLCoS phase modulator 500. FIGS. 23-25 show examples of the LUT map 15.To simplify the description, the value for r in these examples is 4 inFIG. 23, 8 in FIG. 24, and 5 in FIG. 25.

In the examples of the LUT map 15 shown in FIGS. 23-25, the bold linesdelineate regions including all pixels, while the thin lines delineateregions corresponding to one pixel. In FIG. 23, one of the group numbersA-D has been assigned to each pixel. In FIG. 24, one of the groupnumbers A-H has been assigned to each pixel. In FIG. 25, one of thegroup numbers A-E has been assigned to each pixel. In FIGS. 24 and 25,the same group number has been assigned to pixels positioned in regionsdelineated by dotted lines.

FIG. 26 shows an example of one of the r LUTs 51. As shown in FIG. 26,the LUT 51 shows correlations between values t_(a) (first values) fromwhich the control input values A can be selected and values t_(b)(second values) of DA input values B selected to correspond to thecontrol input values A.

The FIG. 26 also indicates an average value φ_(ave) of phase modulationamounts φ attained by whole pixels belonging to a group corresponding tothe LUT 51 when the drive section 321 converts the value t_(b) selectedfor the DA input value B to a corresponding voltage value and applies avoltage of this value to the pixels belonging to the group. The averagevalue φ_(ave) in FIG. 26 is given by the average value of the measuredphase modulation amounts φ. It is noted that LUTs 51 does not includethe average value φ_(ave). The values t_(a) taken as the control inputvalues A and the average values φ_(ave) of phase modulation amounts havea linear relationship. Moreover, the values t_(b) selected for the DAinput values B are set such that the average values φ_(ave) of phasemodulation amounts corresponding to each t_(a) to be taken as thecontrol input values A are substantially equal in all r LUTs 51.Specifically, the values t_(b) are set so that φ_(ave)=1.5 for t_(a)=0,φ_(ave)=1.508 for t_(a)=1, etc.

Hence, the drive unit 530 converts a control input value A to a DA inputvalue B for a pixel belonging to the group with the corresponding LUT 51and converts the DA input value B to an analog signal C and inputs theanalog signal C to the LCoS spatial light modulator 2. As a result, thephase modulation amount φ obtained at that pixel has a substantiallylinear relationship with the control input value A, with littleirregularity among groups.

The calibration pattern 12, LUTs 51, and LUT map 15 are stored in ROM(not shown) in the drive unit 530 and are read into the RAM 538 and RAM539 when the LCoS phase modulator 500 is started. Alternatively, thecalibration pattern 12, LUTs 51, and LUT map 15 may be saved on the HDD44 of the control unit 4 and may be transferred to the drive unit 530and loaded in the RAM 538 and RAM 539 when the LCoS phase modulator 500is started. Further; the RAM 538 and RAM 539 may be integrated into asingle RAM for loading the calibration pattern 12, LUT map 15, and LUTs51.

The LCoS phase modulator 500 having the above construction performsphase modulation according to the operations shown in FIG. 27. In S101of FIG. 27, the communication unit 533 receives the input data ofdesired pattern 13 from the control unit 4 and transfers the input dataof the desired pattern 13 to the processing unit 531. In S102 theprocessing unit 531 transmits position data for each pixel to the pixelposition detector 537. In S103 the pixel position detector 537references the LUT map 15 based on the position data for each pixel toidentify the group number of the group to which each pixel belongs. InS104, the pixel position detector 537 transmits, to the LUT processor536, position data for a pixel and the LUT 51 corresponding to the groupnumber identified for the pixel. The pixel position detector 537performs this transmission for all pixels.

In parallel with the process in S102, the processing unit 531 alsotransmits the input data of the desired pattern 13 to the adder 535 inS105. In S106 the adder 535 adds the pixel input values in the desiredpattern 13 to the correction input values in the calibration pattern 12for each pixel and folds back the phase of the sums when necessary. Thevalues obtained in this process are set as the control input values Acorresponding to the position data for the corresponding pixels. In S107the LUT processor 536 converts the control input values A to DA inputvalues B for each pixel while referencing the LUT 51 received from thepixel position detector 537 in S104. In S108 the drive section 321converts the DA input values B to analog signals C and outputs theanalog signals C to the LCoS spatial light modulator 2.

In parallel with the processes of S101 and S105, the processing unit 531generates a digital signal required for driving the LCoS spatial lightmodulator 2 in S109.

In S110 the LCoS spatial light modulator 2 modulates the phase ofincident light based on the analog signals C received from the drivesection 321 in S108 and the digital signal received from the processingunit 531 in S109.

When manufacturing the LCoS phase modulator 500, the drive section 321,LUT map 15, LUTs 51, and calibration pattern 12 are set in correspondeach with the LCoS spatial light modulator 2 provided in the LCoS phasemodulator 500. The drive unit 530 also stores the program forimplementing a process shown in the flowchart of FIG. 27 in the ROM (notshown). These settings are made based on the following procedureperformed in the order given. First, minimum and maximum voltages Q andR are set for the working voltage range Q-R of the D/A circuit 532.Next, the LUT map 15 is created, after which the LUTs 51 are createdbased on the LUT map 15. Further, the calibration pattern 12 is created.Finally, the program for implementing a process shown in the flowchartof FIG. 27 is stored in the ROM (not shown) of the drive unit 530.

The method of setting the drive section 321 is identical to the methoddescribed in FIG. 8 of the first embodiment. Specifically, the drivesection 321 is set for linearly converting the DA input values B from 0to 4,095 to analog signals C indicating voltage values within theworking voltage range Q-R.

Next, a method of creating the LUT map 15 will be described withreference to FIG. 28. In S111 of FIG. 28, the LCoS phase modulator 500is disposed in the polarization interferometer 60 shown in FIG. 9, andthe polarization interferometer 60 is used to find the relationshipbetween DA input values B and voltage-dependent phase modulation amountsfor each pixel of the LCoS spatial light modulator 2. This measurementprocess is identical to S21 described in FIG. 12. Specifically,measurements are repeatedly performed while varying the DA input value Bfrom 0 to 4,095.

In S112 the least-squares method or the like is used in the followingpolynomial of equation (11) to approximate the relationship between thephase modulation amounts φ and the DA input values (t_(b)) based on theDA input values-phase modulation characteristics found for each pixel inS111. The relationship t_(b)(φ) in equation (11) is found for allpixels.

$\begin{matrix}{{t_{b}(\varphi)} = {{f(\varphi)} = {\sum\limits_{k = 0}^{K}{a_{k}\varphi^{k}}}}} & (11)\end{matrix}$

In S113 a relationship is obtained between the DA input value B and thevalue obtained by averaging out the phase modulation amounts φ that allpixels attain when being applied with a voltage corresponding to the DAinput value B. More specifically, first an average value of phasemodulation amounts for all pixels is obtained for each DA input value B.From these values, the relationship between each DA input value B and anaverage value φ of phase modulation amounts is found throughapproximation. For example, the relationship can be obtained using aK-th polynomial, such as that in equation (12) below, where t_(b,ave)(φ)represents the DA input value B.

$\begin{matrix}{{t_{b,{ave}}(\varphi)} = {\sum\limits_{k = 0}^{K}{a_{k,{ave}}\varphi^{k}}}} & (12)\end{matrix}$

In S114 a Root Mean Square (RMS) value ε₁ (hereinafter referred to as afirst RMS value) for the DA input values t_(b,ave)(φ) for averaged phasemodulation amounts, found in equation (12), and the DA input valuest_(b)(φ) are found for each pixel using equation (13) below.

$\begin{matrix}{ɛ_{1}( {\int_{0}^{2\pi}{{{{r_{b,{ave}}(\varphi)} - {t_{b}(\varphi)}}}^{2}{\varphi}}} )}^{1/2} & (13)\end{matrix}$

Next, the pixel having the largest first RMS value 61 (max RMS pixel)among all pixels is found. The max RMS pixel is determined to be thepixel whose phase modulation amount φ is furthest separated from theaverage phase modulation amount of all pixels.

In S115 a Root Mean Square value E2 (hereinafter referred to as a secondRMS value) for the DA input values of the max RMS pixel (hereinafterreferred to as t_(MAX)(φ)) and the DA input values t_(b)(φ) are foundfor each pixel using equation (14) below.

$\begin{matrix}{ɛ_{2} = ( {\int_{0}^{2\pi}{{{{t_{MAX}(\varphi)} - {t_{b}(\varphi)}}}^{2}{\varphi}}} )^{1/2}} & (14)\end{matrix}$

In S116 the maximum value of the second RMS value ε₂ among all pixels isfound. The minimum value of the second RMS values ε₂ found for allpixels is 0 because t_(b)(φ)=t_(MAX)(φ) for the max RMS pixel. A rangebetween the maximum value and the minimum value of the second RMS valueε₂ is divided into r divisions at even intervals. Next, pixels having asecond RMS value ε₂ belonging to the same division are combined in asingle group for each division, thereby configuring one group for eachdivision and distributing all pixels among r=20 groups. Subsequently,the relationship between pixels and the groups to which the pixelsbelong is saved in the LUT map 15.

In this way, the LUT map 15 is configured by combining pixels belongingto the same division in a single group, where pixels in a division havea similar amount ε₂ indicating the voltage-dependent phase modulationcharacteristics of the pixel. Hence, this method makes it possible tocombine pixels having similar voltage-dependent phase modulationcharacteristics in a single group.

The example of the LUT map 15 shown in FIG. 23 is created for oneexample of the LCoS spatial light modulator 2 in which pixels havingsimilar voltage-dependent phase modulation characteristics aredistributed substantially uniformly throughout the entire pixel region.Hence, pixels belonging to groups A-D have been distributedsubstantially uniformly throughout the entire pixel region. The exampleof the LUT map 15 shown in FIG. 24 is created for another example of theLCoS spatial light modulator 2 in which adjacent pixels have similarproperties. Pixels within regions delineated by dotted lines havesimilar characteristics and thus belong to the same group.

Further, depending on the phase modulation characteristics of the LCoSspatial light modulator 2, adjacent pixels as well as pixels inseparated regions may be included in the same groups, as in groups A, B,and C shown in FIG. 25.

The method of grouping pixels employed in S116 described above may bemodified to one of the following methods [1]-[6].

[1] When dividing pixels into groups according to the above method,there are some cases in which all pixels are not uniformly distributedamong the r groups, depending on the characteristics of the LCoS spatiallight modulator 2. In other words, it is possible that the number ofpixels belonging to each group may deviate greatly from T/r. With method[1], it is possible to distribute all pixels among r groups withrelative uniformity. That is, the number of pixels belonging to eachgroup can be set to approximately T/r. Specifically, the method ofdividing pixels into groups in S116 is modified as follows. First, thesecond RMS values ε₂ obtained for all pixels are arranged in ascending(or descending) order. In other words, the second RMS values ε₂ for allpixels are arranged in a sequence. This sequence is partitioned atsubstantially fixed intervals, forming r segments of the entire series.As a result, the number of pixels included in one segment isapproximately T/r, with the number of pixels in each segmentapproximately equal.

[2] It is also possible to preset the reference value t_(MAX)(φ). Inthis case, S113 and S114 are not executed.

[3] When it is known that a certain pixel has remarkably differentproperties from the other pixels when manufacturing the LCoS spatiallight modulator 2, this pixel has the greatest value of all first RMSvalues ε₁. In this case, the value obtained from equation (11) for thispixel can be set as the reference value t_(MAX)(φ), and S113 and S114are not executed.

[4] In S114 it is also possible to find the phase modulation amount φfor only a certain single DA input value B (the minimum value 0, forexample) for each pixel. In this method, the processes in S112 throughS115 are skipped, and the pixels are grouped in S116 based on themeasured phase modulation amounts φ. Here, the phase modulation amountsφ for all pixels are arranged in ascending (or descending) order, i.e.the phase modulation amounts φ are arranged in a sequence. The sequenceof phase modulation amounts φ is partitioned at fixed intervals,producing r segments. Accordingly, T/r phase modulation amounts φ arearranged in a single segment. Pixels that attain the phase modulationamounts φ included in the same segment are combined in the same group.Hence, T/r pixels attaining a similar phase modulation amount relativeto the same DA input value B can be combined in the same group, therebydistributing a substantially equal number of pixels in each group.

Further, instead of arranging the phase modulation amounts φ for allpixels in ascending order or descending order, the range of phasemodulation amounts between a maximum value and minimum value may bedivided into r segments or equal length. Pixels having a phasemodulation amount φ of a value in the same segment are combined in thesame group. However, in this case, the number of pixels belonging to asingle group may deviate greatly from T/r.

[5] In S111 it is possible to use a DA input value for a specified pixelinstead of the DA input average value t_(b,ave)(φ). In this case, thefirst RMS value is obtained by modifying equation (13) as shown in afollowing ε₁′. Here t_(b,0)(φ) represents the DA input value forspecified pixel.

ɛ₁^(′) = (∫₀^(2π)t_(b, 0)(φ) − t_(b)(φ)²φ)^(1/2)

In the above-described embodiment, pixels are grouped by the scalarquantization. However, the method of grouping pixels is not limited tothe methods described above. For example, after finding the results inequation (11) for all pixels, vector quantization, or another type ofscalar quantization may be used to divide pixels with similar propertiesinto r groups.

Next, a method of creating the LUT 51 for each group will be describedwith reference to FIG. 29. In FIG. 29, S121-S127 are identical toS21-S27 in the first embodiment when creating the LUT 11 for each pixel.Thus, the LUT 11 is created for each pixel in the same manner as the LUT11 is created in the first embodiment. Accordingly, in S121-S127, valuesare found using equations (3)-(10), as described in the firstembodiment. Data acquired for each pixel through equations (3)-(10) istemporarily stored in the HDD 44.

More specifically, in S124 the LUTs 11 are saved in the HDD 44 for eachpixel and are temporarily used for finding the LUT 51 for each group.When subsequently measuring phase modulation amounts in S125, the LUTs11 corresponding to positions of pixels specified by the pixel positiondetector 537 are read from the HDD 44 and transferred to the RAM 539 ofthe drive unit 530.

In S125 the LUT processor 536 converts the control input values A(0-255) to DA input values B based on the LUT 11 for each pixel justobtained in S124, after which the drive section 321 converts the DAinput values B to analog signals C for driving the corresponding pixelsin the LCoS spatial light modulator 2. In S128 a LUT 51 for each groupis created based on the LUTs 11 for each pixel found in S121-S127.

In S128 a LUT 51 is created for each group based on the LUTs 11 obtainedfor all pixels belonging to the group. Specifically, an average value ofphase modulation amounts φ (hereinafter referred to as average phasemodulation amount φ_(g-ave)) acquired for all pixels within a group areobtained for each DA input value (t_(b)). That is, the phase modulationamount φ is measured by using the LUTs 11 for each pixels. The averagephase modulation amount φ_(g-ave) is obtained by averaging the measuredphase modulation amounts φ for all pixels in a group. However, whenpixels in which characteristics of phase modulation amount φ is unusualcompared to pixels in same group are exist, the average phase modulationamount φ_(g-ave) is obtained by averaging the measured phase modulationamount φ for pixels except the unusual pixels in group. The averagephase modulation amount φ_(g-ave) is obtained for each group.

Next, for each group, the relationship between the DA input values t_(b)or the control input values t_(a) and the average phase modulationamount φ_(g-ave) is found through an approximation. The LUT 51 for eachgroup indicating the relationship between the control input values t_(a)and the DA input value t_(b) is found based on this approximation. TheLUT 51 found for each group in this way is stored in ROM (not shown) inthe drive unit 3. Further, the LUTs 11 are deleted from the HDD 44.

Next, a method of finding, for each group, the approximation indicatingthe relationship between the DA input value t_(b) or control inputvalues t_(a) and the average phase modulation amount φ_(g-ave), and therelationship between the control input values t_(a) and DA input valuet_(b) based on this approximation will be described in detail for thefollowing three cases (1)-(3).

(1) In some cases, the process of FIG. 29 may not return from S127 toS123, but may advance to S128 without updating the LUTs 11 acquired frommeasurement results in S122. In these cases, the LUTs 11 are acquiredbased on results of the first measurements.

(2) In some cases, the process of FIG. 29 may return once from S127 toS123, advancing to S128 after performing the process in S125 once. Inthis case, the LUTs 11 are acquired by updating the LUTs 11 based onsecond measurements (i.e., the first measurements performed in S125).

(3) In some cases, the process of FIG. 29 may repeatedly loop back fromS127 to S123 two or more times, advancing to S128 after performing theprocess in S125 two or more times. In these cases, the LUTs 11 areacquired after performing updates based on an M^(th) (where M is anatural number greater than or equal to 3) measurement (i.e., the(M−1)^(th) measurements performed in the process of S125).

<Case (1)>

First, an approximation indicating the relationship between the DA inputvalue t_(b) and the average phase modulation amount φ_(g-ave) acquiredin the first measurement is found as follows.

$\begin{matrix}{t_{b{(1)}} = {{f_{1,{g - {ave}}}( \varphi_{g - {ave}} )} = {\sum\limits_{{k{(1)}} = 0}^{K}{a_{{k{(1)}},{g - {ave}}}\varphi_{g - {ave}}^{k{(1)}}}}}} & (15)\end{matrix}$

In order to achieve a linear relationship between the control inputvalues t_(a) and the average phase modulation amount φ_(g-ave) found inthe first measurement and to express 0.0-2.0π[rad] with 256 levels ofcontrol input values A, the relationship between the control inputvalues t_(a) and average phase modulation amount φ_(g-ave) is expressedas follows, where t_(a)(M) represents the control input values and M=1.

φ_(g-ave) t _(a(M)))=(2π/256)×t _(a(M)) +const  (16)

t_(a)(M) is an integer value from 0 to 255, and const is the same offsetvalue for all groups. The following relationship in equation (17) can beobtained by substituting equation (16) into equation (15).

t _(b(1)) =f _(1,g-ave)(φ_(g-ave)(t _(a(1))))  (17)

Equation (18-1) below is obtained by rounding off the right side ofequation (17).

t _(b(1))=ROUND[f _(1,g-ave)(φ_(g-ave)(t _(a(1))))]  (18-1)

Equation (18-1) indicates the relationship between the DA input values(t_(b(1))) and the control input values (t_(a(1))). The LUT 51 iscreated based on this relationship indicated by equation (18-1).

<Case (2)>

First, an approximation showing the relationship between the previouscontrol input values t_(a) and the current average phase modulationamount φ_(ave) is found as follows, where M=2.

$\begin{matrix}{t_{a{({M - 1})}} = {{f_{M,{g - {ave}}}( \varphi_{ave} )} = {\sum\limits_{{k{(M)}} = 0}^{K}{a_{{k{(M)}},{g - {ave}}}\varphi_{g - {ave}}^{k{(M)}}}}}} & (19)\end{matrix}$

By substituting equation (16) into equation (19) for M=2, the followingrelationship in equation (20) is obtained.

t _(a(M-1)) =f _(M,g-ave)(φ_(g-ave)(t _(a(M))))  (20)

By substituting equation (20) into equation (18-1), the followingequation (18-2) is obtained.

t _(b(2))=ROUND[f _(1,g-ave)(φ_(g-ave)(f _(2,g-ave)(φ_(g-ave)(t_(a(2))))))]  (18-2)

Equation (18-2) indicates the relationship between DA input values(t_(b(2))) and control input values (t_(a(2))). The LUT 51 is createdbased on the relationship indicated by this equation (18-2).

<Case (3)>

Equation (18-3) below is obtained according to the same method describedin Case (2). Accordingly, equation (18-3) is obtained as follows.

t _(b(M))=ROUND[f _(1,g-ave)(φ_(g-ave)(f _(2,g-ave)( . . . f_(M,g-ave)φ_(g-ave)(t _(a(M))))))]  (18-3)

Equation (18-3) indicates the relationship between DA input values(t_(b(M))) and control input values (t_(a(M))), wherein M is greaterthan 2. The LUT 51 is created based on the relationship indicated bythis equation (18-3).

Instead of obtaining an average value φ_(g-ave) for phase modulationamounts φ within a group, it is possible to obtain a value producing theleast amount of variance in phase modulation amounts φ within the groupand to create the LUT 51 based on the value.

The LUT 51 shown in FIG. 26 holds the relationships among the t_(a),t_(b), and average phase modulation amounts φ_(g-ave) obtained for thecorresponding group in the process described above. A linearrelationship can be attained between the control input values A andphase modulation amounts φ for pixels belonging to the subject group byreferencing this LUT 51 when performing the conversion in S107 (FIG.27). Use of the LUT 51 can correct irregularities in phase modulationamounts among each pixel in a group to achieve substantial linearity inthe relationship between the control input values A and the phasemodulation amounts. Moreover, since the equations (18-1), (18-2), or(18-3) are created such that the equation (16) is satisfied for allgroups, irregularities in phase modulation amounts among pixels can becorrected to achieve substantial linearity in the relationship betweenthe control input values A and phase modulation amounts across allpixels and to achieve substantial same phase modulation amounts for thesame control input values A.

After creating the LUT 51 for each group according to the above method,the calibration pattern 12 is created. The method of creating thecalibration pattern 12 is identical to the method of creating thecalibration pattern according to the first embodiment described withreference to FIG. 15. That is, in S31 the drive unit 530 stores apattern having 0s for all pixel values in the RAM 538 as the initialcalibration pattern 12. In S32 the CPU 41 sets the desired pattern 13 toan image in which all pixel values are identical within 0-255, andtransmits the desired pattern 13 to the drive unit 530. The pixel inputvalues in the desired pattern 13 received in the drive unit 530 aretransferred to the adder 535, while position data for pixels in thedesired pattern 13 are transferred to the pixel position detector 537.The pixel position detector 537 identifies corresponding LUTs 51 basedon the position data. In S33 and S41, the adder 535 adds the pixel inputvalues in the desired pattern 13 to the pixel correction values in thecalibration pattern 12 and sets the control input values A to the sums,after folding back the phase if needed. In S34 and S42, the LUTprocessor 536 converts the control input values A to DA input values Bbased on the identified LUTs 51 and transfers the DA input values B tothe D/A circuit 532. In S35 the drive section 321 generates the analogsignals C based on the DA input values B and applies a working voltageto the LCoS spatial light modulator 2 based on the analog signals C. InS39 the phase values (phase modulation amounts) for each pixel in thecalibration pattern 12 are converted to control input values whilereferencing the equation (4) or (7), data of which are stored in the HDD44, and re-expressed in one of 256 levels. It is also possible to storedata for the average phase modulation amounts in the LUT 51 as shown inFIG. 26 and to obtain the calibration pattern in 256 levels expressionby using this LUT 51. In S40 the calibration pattern 12 expressing theacquired phase values in 256 levels is stored in ROM (not shown).

In the LCoS phase modulator 500 according to second embodiment describedabove, all pixels are distributed among a plurality of groups based ontheir phase modulation characteristics, and the same LUT 51 is used forall pixels within a single group. Since there is no need to have a LUT51 for each pixel, the phase modulation characteristics for all pixelscan be corrected efficiently with less data. Hence, the LUTs 51 can bestored on the drive unit 3, even when the drive unit 3 is a type thatcannot easily be equipped with high-capacity memory (RAM).

Further, since the LUTs 51 are stored in the drive unit 530, dedicatedhardware (the adder 535, pixel position detector 537, and LUT processor536) are used to perform (i) the process for adding the desired pattern13 to the calibration pattern 12 and folding back the phase whennecessary (performed on the adder 535), (ii) the process for acquiringpixel position data (performed on the pixel position detector 537), and(iii) the process for converting the control input values A to DA inputvalues B based on the LUTs 51 and for outputting the DA input values Bto the LCoS spatial light modulator 2 (performed on the LUT processor536). The processing time required for processes (i)-(iii) performed onthe drive unit 3 can be reduced, for example, over the processing timerequired for the same processes performed by the CPU 41 on the controlunit 4, thereby enabling the processes to be completed within one frame.

The LUT map 15 provides correlations between the pixel position data andgroup numbers, making it possible to reliably select a LUT 51 suited tothe characteristics of a pixel when performing phase modulation.

The LCoS phase modulator 500 according to the second embodimentdescribed above controls the LCoS spatial light modulator 2 for DA inputvalues B expressed in 4,096 levels within the working voltage rangesmaller than the operable voltage range that ensures the required rangeof the phase modulation amounts. Hence, the LCoS phase modulator 500 cancontrol the voltages applied to the LCoS spatial light modulator 2 withgreat accuracy. Moreover, the LCoS phase modulator 500 employs the LUTs51 to achieve a substantially linear relationship between the controlinput values A and the voltage-dependent phase modulation amounts andcorrects irregularities among pixels caused by voltage-dependent phasemodulation amount, thereby obtaining the desired phase modulationamounts with great accuracy. Further, the LCoS phase modulator 500 usesthe calibration pattern 12 to correct voltage-independent distortion toachieve more accurate phase modulation.

It was found that the output wavefront could be measured with greaterprecision when performing correction using the LUT map 15, LUTs 51, andcalibration pattern 12 in the preferred embodiment than either (i) whenperforming no correction, or (ii) when performing correction using asingle LUT 51 and calibration pattern 12 for all pixels. For example,RMS values for a control input value-measured phase modulationcharacteristics and a control input value-ideal phase modulationcharacteristics are as shown in a following table.

(i) no (ii) single First Second correction LUT embodiment Embodiment RMS0.70λ 0.10λ 0.01λ 0.05λ value

As shown in this table, the phase modulation characteristics becomeaccurate by using the LUTs 11 or 51 and the calibration pattern 12.Though the correction of the first embodiment gives highest accuracy,the correction of the second embodiment gives enough accuracy formeasurement. In fact, a pattern of concentric circles can be seensimilar to FIG. 17(A) when phase modulation for a Laguerre-Gaussian beamis measured on the LCoS phase modulator 500 by using the LUTs 51 and thecalibration pattern 12.

Further, when creating the LUTs 51 and when creating the calibrationpattern 12, the process is repeated until either the required precisionis obtained or until an improvement in precision is not obtained. Thus,it is possible to obtain highly accurate LUTs 51 and a highly accuratecalibration pattern 12 capable of accurately correctingvoltage-dependent phase modulation characteristics andvoltage-independent distortion.

First Variation of the Second Embodiment

It is also possible to use the LCoS spatial light modulator 120 shown inFIG. 18 instead of using the LCoS spatial light modulator 2.

Second Variation of the Second Embodiment

The functions of the control unit 4 may also be incorporated in thedrive unit 530. In this case, the RAM 538 also stores the desiredpattern 13. The desired pattern 13 is saved in ROM (not shown) in thedrive unit 530 and read into the RAM 538 when the LCoS phase modulator500 is started.

Third Variation of the Second Embodiment

In the LCoS phase modulator 500 according to the preferred embodimentdescribed above, the calibration pattern 12 is stored in the RAM 538 ofthe drive unit 530, and the adder 535 adds the pixel input values in thedesired pattern 13 to the pixel correction values in the calibrationpattern 12. However, as in the example of the LCoS phase modulator 600shown in FIG. 30, the desired pattern 13 and calibration pattern 12 maybe stored in the HDD 44, read into the memory unit 43, and added in thecontrol unit 4. In this case, the CPU 41 includes the input valuesetting unit 47 that functions to add the pixel input values of thedesired pattern 13 to the pixel correction values of the calibrationpattern 12. A drive unit 630 of the LCoS phase modulator 600 is notprovided with an adder or RAM for storing the calibration pattern.Specifically, the drive unit 630 includes a communication unit 633, aprocessing unit 631, a pixel position detector 637, an LUT processor636, a D/A circuit 632, and a RAM 639. Of these, the communication unit633 and D/A circuit 632 are identical to the communication unit 33 andD/A circuit 32 shown in FIG. 2. The RAM 639 stores the LUT map 15 andthe LUTs 51, and the D/A circuit 632 is provided with the drive section321.

For phase modulation, the input value setting unit 47 adds the pixelinput values of the desired pattern 13 to the pixel correction values ofthe calibration pattern 12 and sets the control input values A to thesesums, after folding back the phase in the sums when necessary. Thecommunication unit 42 transmits the control input values A and pixelposition data to the drive unit 630. The communication unit 633transfers the control input values A and pixel position data to theprocessing unit 631. The processing unit 631 transfers position data ofpixels to the pixel position detector 637 and transfers the controlinput values A for these pixels to the LUT processor 636. Thereafter,the LUT processor 636 and the D/A circuit 632 perform the same processas the processor 536 and the D/A circuit 532 according to the secondembodiment to modulate the phase of incident light on the LCoS spatiallight modulator 2. Since the LCoS phase modulator 600 described abovedoes not need to add the calibration pattern 12 and desired pattern 13in the drive unit 630, it is possible to reduce the capacity of RAMprovided in the drive unit 630.

Fourth Variation of the Second Embodiment

It is also possible to save the desired pattern 13, calibration pattern12, LUTs 51, and LUT map 15 in the HDD 44, read this data into thememory unit 43, and find and transmit the DA input values B to the driveunit 3, as in a LCoS phase modulator 700 shown in FIG. 31. In thisconstruction, the CPU 41 includes a converter 46, an input value settingunit 47, and a pixel position detector 48. The drive unit 3 is identicalto the drive unit 3 shown in FIG. 2.

For phase modulation, the input value setting unit 47 adds the pixelinput values of the desired pattern 13 to the pixel correction values ofthe calibration pattern 12, setting the sums as the control input valuesA after performing phase fold-back when necessary. The pixel positiondetector 48 references the LUT map 15 to identify group numberscorresponding to the pixel position data. The converter 46 converts thecontrol input value A for each pixel to a DA input value B using the LUT51 corresponding to the identified group number. The communication unit42 transmits the DA input values B to the drive unit 3. Thecommunication unit 33 transfers the DA input values B received from thecommunication unit 42 to the processing unit 31. The remaining processis identical to that described in the first embodiment for modulatingthe phase of incident light on the LCoS spatial light modulator 2. Withthe LCoS phase modulator 700 having this configuration, the drive unit 3need not be provided with RAM for saving the desired pattern 13, LUTs51, LUT map 15, and calibration pattern 12, thereby reducing the cost ofthe device.

Fifth Variation of the Second Embodiment

While the D/A circuit 532 is provided in the drive unit 530 in thesecond embodiment described above, the D/A circuit may be separated fromthe drive unit 530, and the LCoS spatial light modulator may be providedwith the D/A circuit and a reception circuit for receiving the DA inputvalues B. With this construction, the drive unit 530 transfers the DAinput values B to the reception circuit on the LCoS side.

Sixth Variation of the Second Embodiment

Further, in the drive unit 530 of the second embodiment, the RAM 539stores the LUT map 15 and the LUTs 51. However, another RAM may bedirectly connected to the LUT processor 536 and may stores the LUTs 51.In this case, the RAM 539 only store the LUT map 15. In the secondembodiment, the LUTs 51 are read into the LUT processor 536 via thepixel position detector 537. However, in this variation, the LUTprocessor 536 reads the LUTs 51 directly from the other RAM. With thisconfiguration, the pixel position detector 537 transmits to the LUTprocessor 536 data indicative of the LUTs 51 identified with referenceto the LUT map 15. The LUT processor 536 performs an LUT process(process for converting the control input values A to DA input valuesB), while referencing the LUTs 51 stored in the other RAM according tothe data received from the pixel position detector 537.

Seventh Variation of the Second Embodiment

While the drive unit 530 shown in FIG. 22 is provided with only one D/Acircuit 32, the drive unit 530 may be given a plurality of D/A circuits532 for simultaneously outputting a plurality of analog signals C to theLCoS spatial light modulator 2 in order to simultaneously write analogsignals to a plurality of pixels. In the drive unit 530 having thisconstruction, the process circuit of the drive unit 530 is configured tosimultaneously output DA input values B for a plurality of pixels to theD/A circuits 532.

Eighth Embodiment of the Second Embodiment

The D/A circuit 532 may also be replaced with a pulse modulationcircuit. With this construction, the pulse modulation circuit outputs adigital pulse modulation signal for driving the LCoS spatial modulator.

Ninth Variation of the Second Embodiment

Further, it is possible to save data for the approximating polynomialsfound in equations (15), (16) and (19) (coefficients a_(k(I),g-ave),where 1≦I≦J, and value “const”), as sets of reference data, in the ROM(not shown) in the drive unit 530 instead of the LUTs 51. As in themethod of creating the LUTs 51 in the second embodiment (S128),depending on a number of times to return to S123, the equations(18-1)-(18-3) are obtained by using this data. Hence, the relationshipbetween the control input values A and DA input values B can be obtainedfrom the equations (18-1)-(18-3). When measuring the phase modulationamount, the LUT processor 536 converts control input values A to DAinput values B based on this data (S107). Other various types of sets ofreference data can be employed instead of the LUTs 51 ore thecoefficients for the approximating polynomials.

Tenth Variation of the Second Embodiment

When creating the LUTs 51 and the LUT map 15 in the preferred embodimentdescribed above, measurements are performed for all pixels. However, itis also possible to measure phase modulation amounts only forrepresentative pixels rather than all pixels. For example, blocks may beconfigured of a plurality of neighboring pixels, where one blockincludes 4×4 pixels, for example. One pixel in each block is set as areference pixel, and measurements are only performed on therepresentative pixels. All the blocks are divided into several groupsbased on the results of these measurements, and the LUT map 15 iscreated to indicate these groups. More specifically, the LUT map 15indicates the relationship between blocks and the LUTs 51 correspondingto the blocks. In this example, the same LUT 51 is applied to all pixelswithin a single block.

Eleventh Variation of the Second Embodiment

As shown in FIG. 32, the values of the calibration pattern 12 may beincluded in the LUTs 51. This variation is similar to the variation ofthe seventh variation of the first embodiment shown in FIG. 21. That is,data for correcting voltage-independent distortion can be included inthe LUT 51 by shifting the reference position in the LUT 51 for eachgroup by a value in the calibration pattern for the one pixel thatbelongs to the subject group. Or, this shifting value may be an averagevalue for all pixels in the calibration pattern in the subject group.FIG. 32 has included data for correcting voltage-independent distortionin the data of FIG. 26, with p=64. For example, the value of t_(b) is1,050 when t_(a) is 0 in the table of FIG. 26, but this value of t_(b)appears when t_(a) is 64 in FIG. 21.

In this case, the drive unit 530 in FIG. 22 need not include the adder535 and the RAM 538. Further, steps S106 are not required in the phasemodulation method described with reference to FIG. 27. Thus, the processunit 531 transmit the input values to the LUT process unit 536. The LUTs51 that include the values of calibration pattern 12 as shown in FIG. 32are used in S103, 104, and 107. Hence, the drive unit 530 can alsocorrect voltage-independent distortion simply by applying the LUTs 51that include the calibration pattern, thereby eliminating the need tosave the calibration pattern and to perform a process to add thecalibration pattern to the desired image.

The LUTs 51 including the calibration pattern can be created by units ofblocks. The LUTs 51 are divided into blocks according to the same methoddescribed above. In this case, the phase modulation characteristics aremeasured for at least one pixel in a block, and the correction value foreach pixel in the block is set to the average value of correction valuesfor each pixel that are found in the block. Alternatively, when thephase modulation characteristics are measured for only one pixel in ablock, the correction value for the block may be simply set to thecorrection value for that pixel rather than an average value. The sizeand position of the blocks in the LUTs 51 and the calibration pattern 12are identical to each other. The value for each block in the calibrationpattern 12 is simply reflected in the corresponding block constitutingthe LUTs 51.

In this way, data in the calibration pattern 12 can be included in theLUTs 51 for correcting voltage-independent distortion while the LUTs 51are used to convert control input values A to DA input values B.Therefore, the process of adding the calibration pattern 12 may beomitted, achieving more efficient phase modulation.

Twelfth Variation of the Second Embodiment

Distortion does not occur in the glass substrate 25 of the LCoS spatiallight modulator 2 since the glass substrate 25 is made considerablythick (3 mm, for example). The problem of distortion occurs only in thesilicon substrate 21, as illustrated in FIG. 33(A). The orientationlayers 23 and electrode 24 have been omitted from the drawings in FIGS.33(A) (and 33(B), described later). The thickness of the liquid crystallayer 27 shown in FIG. 33(A) varies according to distortion in thesilicon substrate 21, as indicated by distances d1 and d2.

Pixels have the same phase modulation amounts when the correspondingregion of the liquid crystal layer 27 has the same thickness so as toapply an equal voltage. Based on this knowledge, if the glass substrate25 is formed thick and the shape of distortion in the silicon substrate21 is known, it is possible to determine which pixels have the samephase modulation amounts. Hence, in place of the method for creating theLUT map 15 shown in FIG. 28, the LUT map 15 can be found by measuringquantities indicating the distorted shape of the silicon substrate 21according to one of the following three methods 1-3, for example.

1. This method will be described with reference to FIG. 34. In S131 ofFIG. 34, LUTs 11 are created for all pixels. Specifically, the processesin S121-S127 shown in FIG. 29 are executed. In S132 the Michelsoninterferometer 80 shown in FIG. 14 is used to measure the phasemodulation amounts Φ. More specifically, the control input values A thesame for all pixels are converted to a DA input values B using the LUTs11, the DA input values B are converted to analog signals C, and theanalog signals C are applied to the LCoS spatial light modulator 2. InS133 a pixel that has attained the maximum phase modulation amount and apixel that has attained the minimum phase modulation amount are found.In S134 the range between the minimum and maximum values of the phasemodulation amounts is divided into r segments at even intervals, andpixels having phase modulation amounts within the same segment arecombined in the same group. The relationship between the groupsconfigured above and their pixels is saved in the LUT map 15.

In this method, the Michelson interferometer 80 is used to measure thephase modulation amounts Φ after converting the control input values Ato DA input values B with LUTs 11 for each pixel, thereby correcting thevoltage-dependent phase modulation characteristics. Hence, this methodcorrects the phase modulation amount φ that depends on voltage V asshown in equation (1), removing irregularities among pixels. Therefore,irregularities in the measured phase modulation amount Φ for each pixelmean the irregularity of Φ₀ for each pixel, where Φ₀ is a quantityindicating distortion in the silicon substrate. Hence, all pixels in theLUT map 15 created according to this method have been grouped accordingto the voltage-independent phase modulation characteristics indicatingdistortion in the silicon substrate.

2. In this variation, the method of creating the LUT map 15 described inFIG. 28 is modified as follows. According to the second embodiment, inS111 of FIG. 28, the polarization interferometer 60 in FIG. 9 is used tomeasure phase modulation amounts while applying the same voltage to allthe pixels in the LCoS spatial light modulator 2 based on the same DAinput value B. These measurements are repeated while varying the DAinput value B from 0 to 4,095. In this variation, the Michelsoninterferometer 80 shown in FIG. 14 is used in place of the polarizationinterferometer 60. Further, the Michelson interferometer 80 measuresphase modulation amounts while applying the same voltage to all thepixels in the LCoS spatial light modulator 2 based on the same DA inputvalue B. This measurement is performed while applying a voltage valuecorresponding to only a single DA input value B falling between 0 and4,095, and the processes in S112-S115 are not executed. In S116 minimumand maximum values are found from the phase modulation amounts acquiredin S111 for all pixels, and a range of maximum and minimum values of thephase modulation amounts is divided into r segments. Pixelscorresponding to phase modulation amounts belonging to the same segmentare combined into a single group. The LUT map 15 is then created byfinding the relationships between these pixels and their groups.

In this method, the Michelson interferometer 80 is used to measure thephase modulation amounts Φ, without using the LUTs 11 for each pixel.Hence, the measured phase modulation amounts Φ include the quantity φdependent on voltage in equation (1). As indicated in equation (2), φ isdependent on the thickness d(x, y) of the liquid crystal layer 27. For aLCoS spatial light modulator 2 having no distortion in the glasssubstrate 25, the thickness d(x, y) of the liquid crystal layer 27 is aquantity indicating distortion in the reflecting surface. Hence, findingΦ in equation (1) is equivalent to finding a quantity related todistortion in the silicon substrate 21. Therefore, this method groupspixels based on their voltage-independent phase modulationcharacteristics indicating distortion in the silicon substrate 21.

3. Similarly to the method 2 above, in S111 the Michelson interferometer80 of FIG. 14 is used to measure the phase modulation amount Φ achievedby each pixel. A pattern is created based on the results of thesemeasurements for achieving uniform values of the phase modulation amountΦ in all pixels, and the LUT map 15 is created using this pattern.Specifically, the DA input value B is sequentially set to all valuesfrom 0 to 4,095. Every time the DA input values B is set to one of thevalues of 0-4095, each pixel is driven with the corresponding analogsignal C. A pattern showing the distribution of DA input values B isfound based on the acquired phase modulation amounts. This pattern is adistribution of DA input values B that have caused the pixels to attainthe same amounts of phase modulation. The processes in S112-S115 are notexecuted in this method. In S116 minimum and maximum values are foundfor the DA input values B distributed in the pattern found in S111, anda range between minimum and maximum values of the DA input values B isdivided into r segments, and pixels attaining phase modulation amountswithin the same segment are combined in the same group. The LUT map 15is then created by finding the relationship between the pixels and theirgroups. This method can group the pixels according to theirvoltage-independent phase modulation characteristics indicatingdistortion in the silicon substrate 21.

In the above methods 1-3, the voltage independent distortion is measuredby the Michelson interferometer 80 and the pixels are grouped based onthe liquid crystal layer thickness d(x, y) of the liquid crystal layer27. However, the measuring method is not limited to the above methods.It is possible to group the pixels by measuring quantities that showdifferences of the liquid crystal layer thickness d(x, y). Thus, basedon the measured quantities, the LUT map is created as the same method ofthe above method 1-3. For example, the liquid crystal layer thicknessd(x, y) for each pixel position may be optically measured.

Methods 1-3 can group pixels in a manner that reflects quantitiesindicating distortion in the silicon substrate 21.

Thirteenth Variation of the Second Embodiment

If, as illustrated in FIG. 33(B), the glass substrate 25 is tilted inany of the three methods in the twelfth variation described above, it ispreferable to perform correction considering tilt of the glasssubstrate. If the glass substrate 25 is not tilted, the distortion ofthe silicon substrate 21 shows the differences in thickness of theliquid crystal layer 27, that is, the distortion of the siliconsubstrate 27 shows the differences of the phase modulation amounts amongthe pixels. Thus, pixels are grouped based on the distortion of thesilicon substrate 21. However, if the glass substrate 25 is tilted,distortion in the silicon substrate 21 does not mean differences inthickness of the liquid crystal layer, as illustrated in FIG. 33(B).Thus, the tilt of the glass substrate 25 needs to be considered whengrouping pixels.

When the glass substrate 25 is tilted, pixels are divided into groupsconsidering not only the distortion of the silicon substrate 21 thatrelates to a part of liquid crystal layer thickness (d_(s)(x, y)) butalso irregularities of a part of liquid crystal layer thickness(d_(g)(x, y)) that is caused by the tilt of the glass substrate 25. Itis noted that θ_(x) and θ_(y) represent tilt angles in the bottomsurface of the glass substrate 25 relative to the x and y directions,respectively. In FIG. 33(B), a reference plane S1 is a plane parallel tothe bottom surface of the silicon substrate 21. When the glass substrate25 is not tilted, the bottom surface of the glass substrate 25 matchesthe reference imaginary plane S1. A part of the liquid crystal layerthickness from the top surface of the silicon substrate 21 to thereference plane S1 is represented by d_(s)(x, y), while a part of theliquid crystal layer thickness from the reference plane S1 to the glasssubstrate 25 is represented by d_(g)(x, y). The total of the liquidcrystal layer thickness d(x, y) is given by adding d_(s)(x, y) tod_(g)(x, y).

It is possible to calculate the voltage-dependent phase modulationamount (φ_(g)(V, x, y)) attributed to the part of liquid crystal layerthickness d_(g)(x, y) when the tilt angles θ_(x) and θ_(y) are known.So, d_(g)(x, y) is obtained by calculating following equation (21).

d _(g)(x,y)=L _(x) tan θ_(x) +L _(y) tan θ_(y)  (21)

Here, a reference point O is the point where d_(g)(x, y)=0. L_(x) andL_(y) are distances in the x and y directions, respectively, from thereference point O to the pixel position (x, y).

The voltage-dependent phase modulation amount φ_(g)(V, x, y) iscalculated from the following equation.

φ_(g)(V,x,y)=2Δn(V)d _(g)(x,y)  (22)

So in this variation, the phase modulation amounts Φ₀(x, y) is measuredas quantities that specify the distortion of the silicon substrate 21.To obtain the LUT map 15, at first, the LUTs 11 are created for allpixels similar to the processes in S121-S127 shown in FIG. 29. Next, byusing the Michelson interferometer 80 in FIG. 14, the phase modulationamounts Φ(V, x, y) are measured by applying drive voltages afterconverting the control input values A to DA input values B with the LUTs11 for each pixel. Here, the drive voltage applied to each pixel (x, y)is indicated as V in equation (22). Since the LUTs 11 is used beforemeasurement, irregularities in the voltage-dependent phase modulationamounts φ(V, x, y) are canceled. Thus, irregularities in the measuredphase modulation amounts (Φ(V, x, y)) depend only on the irregularitiesin the voltage independent phase modulation amounts Φ₀(x, y). It isnoted that the measured quantity Φ(V, x, y) does not relate φ_(g)(V, x,y).

In other words, the measured phase modulation amounts Φ(V, x, y) (=Φ₀(x,y)) show distribution in the part of liquid crystal layer thicknessd_(s)(x, y). On the other hands, φ_(g)(V, x, y) is given by calculationsindicative of distribution in the part of liquid crystal layer thicknessd_(g)(x, y). Hence, the phase modulation amounts accounting for tilt arefound by adding phase modulation amounts Φ₀(x, y) measured by theMichelson interferometer 80 to φ_(g)(V, x, y) found from equation (22),and performing fold back process for the phase to the sums. Pixels aregrouped based on the fold backed phase modulation amounts (hereinafter,phase modulation amount accounting for tilt) similarly to the twelfthvariation described above. For example, when grouping pixels in asimilar manner to the twelfth variation, at first, minimum and maximumvalues of phase modulation amounts accounting for tilt are identified. Arange between the minimum and maximum values of the phase modulationamounts accounting for tilt are divided into r segments at evenintervals. Pixels having phase modulation amounts accounting for tilt inthe same segment are grouped together, and the LUT map 15 is createdbased on these groups.

Pixels are thus grouped in a manner that reflects quantities indicatingdistortion in the silicon substrate 21 and the tilt of the glasssubstrate 25.

While the invention has been described in detail with reference to theabove embodiments thereof, it would be apparent to those skilled in theart that various changes and modifications may be made therein withoutdeparting from the spirit of the invention.

Other phase-modulating spatial light modulators may be used in place ofthe LCoS spatial light modulator 2, such as an optically addressablephase modulator, a MEMS phase modulator, deformable mirrors, and ananalog magneto-optic device. One possible optically addressable phasemodulator is described in “High Efficiency Electrically-AddressablePhase-Only Spatial Light Modulator”, Yasunori Igasaki et al., OpticalReview, Vol. 6, No. 4, pp. 339-344, 1999. One possible MEMS phasemodulator is described in “One Megapixel SLM with high optical fillfactor and low creep actuators”, M. Friedrichs et al., Optical MEMS andTheir Applications Conference 2006, IEEE/LEOS International Conferenceon. One analogue magneto-optic device is described in “Magnetophotiniccrystals—a novel magneto-optic material with artificial periodicstructures”, Mitsuteru Inoue et al., J. Mater. Chem. Vol. 16, pp678-684, 2006.

When using a MEMS SLM, voltage-independent distortion appears aswavefront distortion acquired when no voltage is applied. If V=0 inequation (1), then φ(V, x, y)=0 and Φ₀=Φ(0, x, y). Hence, the Φ₀attributed to distortion in the reflecting surface can be found throughmeasurements with the Michelson interferometer 80 in FIG. 14, withoutapplying a voltage. The calibration pattern 12 is created based on Φ₀.Further, the voltage-dependent phase modulation characteristics appearas irregularities in phase modulation amounts among pixels when avoltage is applied. These voltage-dependent phase modulationcharacteristics can be corrected with the LUTs 51 created according tothe method in the second embodiment.

The analog magneto-optic device rotates the polarizing direction ofincident light when voltage is applied. The voltage-independent phasemodulation characteristics indicate irregularities among pixels in therotation of the polarizing direction for light measured by the Michelsoninterferometer 80 in FIG. 14 without the application of voltage. Thevoltage-dependent phase modulation characteristics indicateirregularities among pixels in the rotation amount of the polarizingdirection for light measured with the Michelson interferometer 80 whenvoltage is applied. Hence, the calibration pattern 12 is created basedon the rotation of the polarizing direction measured by the Michelsoninterferometer 80 without applying voltage, while the LUTs 11 or 51 canbe created based on the amount of rotation in the polarizing directionmeasured by the Michelson interferometer 80 when voltage is applied.

In the first and second embodiments the drive section 321 is set suchthat the DA input values B (0-4094) are assigned linearly to the workingvoltage range Q-R based on the voltage-dependent phase modulationcharacteristics. However, the drive unit 321 may remain in initialsetting. That is, the drive unit 321 is set such that the DA inputvalues B (0-4096) are assigned linearly to the operating voltage P-S.

The phase-modulating apparatuses of the above-described embodiments andvariations are suitable for use in laser machining, optical tweezers,adaptive optics, imaging optical systems, optical communications,aspheric lens inspection, pulse shape control for short-pulse lasers,optical memory devices, and the like.

1. A phase-modulating apparatus comprising: a spatial light modulatorincluding a plurality of pixels arranged adjacent to one anothertwo-dimensionally, each pixel being capable of phase-modulating inputlight in response to application of a drive voltage; an input valuesetting unit setting an input value for each pixel; a plurality of setsof reference data, each set of reference data corresponding to at leastone pixel; a converting unit converting an input value inputted for eachpixel to a control value by referencing the corresponding set ofreference data; and a driving unit converting the control value to avoltage value, the driving unit driving each pixel with a drive voltagecorresponding to the voltage value; each set of reference datacorrelating a plurality of first values from which input values aretaken, and a plurality of second values from which control values aretaken to ensure that the relationship between the plurality of firstvalues and phase modulation amounts attained by the corresponding atleast one pixel is a prescribed linear relationship.
 2. Thephase-modulating apparatus as claimed in claim 1, wherein each pixel iscapable of being driven at a voltage value within an operating voltagerange; the driving unit converts the control value to the voltage valuewithin a working voltage range set within the operating voltage rangeand drives each pixel with a drive voltage at the voltage value; and theworking voltage range is set based on voltage-dependent phase modulationcharacteristics for at least one pixel among the plurality of pixels. 3.The phase-modulating apparatus as claimed in claim 1, wherein each setof reference data is in the form of a look-up table, the look-up tablestores one-on-one correspondences between the plurality of first valuesand the plurality of second values.
 4. The phase-modulating apparatus asclaimed in claim 1, wherein the plurality of sets of reference data areprovided in correspondence with units of blocks, each block including atleast one of pixels.
 5. The phase-modulating apparatus as claimed inclaim 4, wherein each block includes at least one pixel that is arrangedadjacent to one another.
 6. The phase-modulating apparatus as claimed inclaim 1, wherein the input value setting unit determines a sum by addingtogether a desired value indicating a desired phase amount and acorrection value indicating a voltage-independent distortion calibrationamount for each pixel and sets the sum as the input value for eachpixel.
 7. The phase-modulating apparatus as claimed in claim 1, whereinthe input value setting unit sets a desired value indicating a desiredphase pattern as the input value for each pixel, each set of referencedata correlating the plurality of first values from which input valuesare taken, and the plurality of second values from which control valuesare taken to ensure that the relationship between sums determined byadding the first values to a correction value indicating avoltage-independent distortion calibration amount, and phase modulationamounts attained by the corresponding at least one pixel is theprescribed linear relationship.
 8. The phase-modulating apparatus asclaimed in claim 1, wherein each set of reference data is repeatedlyrecreated based on measurement results obtained by converting theplurality of input values to a plurality of control values whilereferencing an already-created set of reference data, converting theplurality of control values to the voltage values, and measuring phasemodulation amounts denoting the voltage-dependent phase modulationcharacteristics while driving at least one of the corresponding pixelsby drive voltages at the corresponding voltage values.
 9. Thephase-modulating apparatus as claimed in claim 6, wherein the correctionvalue for each pixel indicating a voltage-independent distortioncalibration pattern is repeatedly recreated based on measurement resultsobtained by using a sum of a phase-indicating value and analready-created correction value for each pixel, converting the sum to acontrol value while referencing the corresponding set of reference data,converting the control value to the voltage value, and measuring thevoltage-independent distortion while driving the each pixel by a drivevoltage at the voltage value.
 10. The phase-modulating apparatus asclaimed in claim 1, further comprising: a reference data map correlatingeach pixel with one of a plurality of groups based on the phasemodulation characteristics of the pixel; and an identifying unitidentifying one set of reference data corresponding to a groupassociated with each pixel using the reference data map; wherein thesets of plurality of reference data have a one-on-one correspondencewith the plurality of groups.
 11. The phase-modulating apparatus asclaimed in claim 10, wherein the reference data map correlates positiondata for each pixel with one set of reference data that corresponds toone group associated with the each pixel.
 12. The phase-modulatingapparatus as claimed in claim 11, wherein the reference data mapcorrelates position data for each pixel with one set of reference datathat corresponds to one group associated with the each pixel based on avalue denoting a difference between voltage-dependent phase modulationcharacteristics of the each pixel and voltage-dependent phase modulationcharacteristics of a reference pixel.
 13. The phase-modulating apparatusas claimed in claim 12, wherein the reference pixel is selected from theplurality of pixels based on a value denoting the difference between thevoltage-dependent phase modulation characteristics of the each pixel andan average of voltage-dependent phase modulation characteristics for theplurality of pixels.
 14. The phase-modulating apparatus as claimed inclaim 10, wherein the spatial light modulator is a liquid crystal onsilicon (LCoS) type spatial light modulator comprising a glass substrateand a silicon substrate; and the reference data map correlates positiondata for the each pixel with one set of reference data corresponding toa group associated with the each pixel based on a value indicatingdistortion in the silicon substrate of the LCoS spatial light modulator.15. The phase-modulating apparatus as claimed in claim 14, wherein thereference data map correlates position data for the each pixel with oneset of reference data corresponding to a group associated with the eachpixel, based on voltage-independent distortion resulting from distortionin the silicon substrate.
 16. The phase-modulating apparatus as claimedin claim 14, wherein the reference data map correlates position data forthe each pixel with one set of reference data corresponding to one groupassociated with the each pixel, based on tilt in the glass substrate anddistortion in the silicon substrate of the LCoS spatial light modulator.17. A method for setting a phase-modulating apparatus that includes, aspatial light modulator including a plurality of pixels arrangedadjacent to one another two-dimensionally, each pixel being capable ofphase-modulating input light in response to application of a drivevoltage, an input value setting unit setting an input value for eachpixel, and a driving unit converting the control value to a voltagevalue, the driving unit driving each pixel with a drive voltagecorresponding to the voltage value, the method comprising: creating aplurality of sets of reference data, the creating step includes:measuring phase modulation amounts, for at least one pixel, denoting thevoltage-dependent phase modulation characteristics; generating aplurality of sets of reference data, based on the voltage-dependentphase modulation characteristics, such that each set of reference datacorresponds to at least one pixel and that each set of reference datacorrelates a plurality of first values from which input values aretaken, and a plurality of second values from which control values aretaken to ensure that the relationship between the plurality of firstvalues and phase modulation amounts attained by the corresponding atleast one pixel is a prescribed linear relationship; and setting theconverting unit to convert, for each pixel, the control value to thevoltage value by referencing the corresponding set of reference data.18. The method as claimed in claim 17, wherein each pixel is capable ofbeing driven at a voltage value within an operating voltage range, themethod further comprising: setting a working voltage range within theoperating voltage range based on a voltage dependent phase modulationcharacteristic for at least one pixel among the plurality of pixels, andsetting the driving unit to convert the control value to a voltage valuewithin the working voltage range.
 19. The method as claimed in claim 17,wherein the generating step generates each set of reference data in theform of a look-up table that stores one-on-one correspondences betweenthe plurality of first values and the plurality of second values. 20.The method as claimed in claim 17, wherein the generating step generatesthe plurality of sets of reference data to be provided in correspondencewith units of blocks, each block including at least one of pixel. 21.The method as claimed in claim 20, wherein each block includes at leastone pixel that is arranged adjacent to one another.
 22. The method asclaimed in claim 17, further comprising: creating a voltage-independentdistortion calibration pattern, the creating the calibration patternstep including; converting a control value to a voltage value whilereferring an already-created set of reference data; measuring a phasemodulation amount denoting voltage-independent phase modulationcharacteristics while driving each pixel by drive voltage at thecorresponding voltage values; and generating the voltage-independentdistortion calibration pattern based on the voltage-independent phasemodulation characteristics.
 23. The method as claimed in claim 22,wherein the input value setting unit determines a sum by adding togethera desired value indicating a desired phase amount and a correction valueindicating a voltage-independent distortion calibration amount for eachpixel and sets the sum as the input value for each pixel.
 24. The methodas claimed in claim 22, wherein the input value setting unit sets adesired value indicating a desired phase pattern as the input value foreach pixel, further comprising shifting the first values in the set ofreference data by a correction value indicating a voltage-independentdistortion calibration amount for the at least one pixel.
 25. The methodas claimed in claim 17, wherein the creating step further including:determining whether the set of reference data should be recreated ornot; recreating the set of reference data if the determining stepdetermines the set of reference data should be recreated, the recreatingstep including; converting control values to voltage values whilereferring an already-created set of reference data; converting theplurality of control values to the voltage values; measuring phasemodulation amounts denoting the voltage-dependent phase modulationcharacteristics while driving at least one of the corresponding pixelsby drive voltages at the corresponding voltage values; and regeneratinga set of reference data based on the voltage-dependent phase modulationcharacteristics obtained by the measuring step of the recreating step.26. The method as claimed in claim 22, the method further comprising:determining whether the voltage-independent calibration pattern shouldbe recreated or not; and recreating the voltage-independent calibrationpattern if the determining step determines the set of reference datashould be recreated, the recreating step includes; summing aphase-indicating value and an already-created correction value for eachpixel; converting the sum to a control value while referencing thecorresponding set of reference data; converting the control value to thevoltage value; measuring the voltage-independent distortion whiledriving the at least one pixel in the corresponding block by a drivevoltage at the voltage value; and regenerating a voltage-independentcalibration pattern based on the voltage-independent distortion obtainedby the measuring step of the recreating step.
 27. The method as claimedin claim 17, wherein the phase-modulation apparatus includes anidentifying unit, the method further comprising; creating a referencedata map, the creating the reference data map step includes: measuringphase modulation amount, for at least one pixel, denoting thevoltage-dependent phase modulation characteristics; and dividing thepixels to a plurality of groups based on the measured phase modulationcharacteristics of the pixels; generating the reference data map tocorrelates each pixel with one of a plurality of groups, wherein thesets of plurality of reference data have a one-on-one correspondencewith the plurality of groups, setting an identifying unit to identifyone set of reference data corresponding to a group associated with eachpixel using the reference data map.
 28. The method as claimed in claim27, wherein the generating the reference data map step generates thereference data map to correlate position data for each pixel with oneset of reference data that corresponds to one group associated with theeach pixel.
 29. The method as claimed in claim 27, wherein the creatingthe reference data map step includes: selecting a reference pixel; andobtaining a first value denoting a difference between voltage-dependentphase modulation characteristics of the each pixel and voltage-dependentphase modulation characteristics of the reference pixel, wherein thegenerating reference data map step generates the reference data map tocorrelate position data for each pixel with one set of reference datathat corresponds to one group associated with the each pixel based onthe first value.
 30. The method as claimed in claim 29, wherein theselecting step includes obtaining a second value denoting the differencebetween the voltage-dependent phase modulation characteristics of theeach pixel and an average of voltage-dependent phase modulationcharacteristics for the plurality of pixels, wherein the selecting stepselects the reference pixel from the plurality of pixels based on thesecond value.
 31. The method as claimed in claim 27, wherein the spatiallight modulator is a liquid crystal on silicon (LCoS) type spatial lightmodulator including a glass substrate and a silicon substrate, thecreating the reference data map step includes obtaining a valueindicating distortion in the silicon substrate of the LCoS spatial lightmodulator, wherein the generating the reference data map step generatesthe reference data map to correlate position data for the each pixelwith one set of reference data corresponding to a group associated withthe each pixel based on the value.
 32. The method as claimed in claim31, wherein the creating the reference data map step includes obtainingvoltage-independent distortion resulting from distortion in the siliconsubstrate, wherein the generating the reference data map step generatesthe reference data map to correlate position data for the each pixelwith one set of reference data corresponding to a group associated withthe each pixel, based on voltage-independent distortion.
 33. The methodas claimed in claim 31, wherein the generating the reference data mapstep generates the reference data map to correlate position data for theeach pixel with one set of reference data corresponding to one groupassociated with the each pixel, based on tilt in the glass substrate anddistortion in the silicon substrate of the LCoS spatial light modulator.